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AP Statistics10/28/08

Test #4 (Chapter 5)

_on n _

Wood/MyersName _

Period _Honor Pledge _

Part 1- Multiple Choice (Questions 1-10) - Circle the letter of the answer of your choice.

1. In a certain community, 20% of cable subscribers also subscribe to the company's broadband service for Internetconnection. You would like to design a simulation to estimate the probability that one of six randomly selectedsubscribers has the broadband service. Using digits 0 through 9, which of the following assignments would beappropriate to model this situation?

(a) Assign even digits as broadband subscribers and odd digits as cable-only subscribers.(b) Assign 0 and 1 as broadband subscribers and 2, 3, 4, 5,6,7, 8,and 9 as cable-only subscribers.(c) Assign 0, 1, and 2 as a broadband subscriber and 3, 4, 5, 6, 7, 8, and 9 as a cable-only subscriber.(d) Assign 1,2,3,4,5, and 6 as a broadband subscriber and 7, 8, 9, and 0 as a cable-only subscriber.(e) Assign 0, 1, and 2 as a broadband subscriber; 3, 4, 5, and 6 as a cable-only subscriber; and ignore digits 7, 8, 9 and O.

2. A cause-and-effect relationship between two variables can best be determined from which of the following?

(a) A survey conducted using a simple random sample of individuals.(b) A survey conducted using a stratified random sample of individuals.(c) When the two variables have a correlation coefficient near 1 or -1.(d) An observational study where the observational units are chosen randomly.(e) A controlled experiment where the observational units are chosen randomly.

3. Which of the following is a true statement about experimental design?

(a) Replication is a key component in experimental design. Thus, an experiment needs to be conducted on repeatedsamples before generalizing results.

(b) Control is a key component in experimental design. Thus a control group that receives a placebo is a requirement forexperimentation.

(c) Randomization is a key component in experimental design. Randomization is used to reduce bias.(d) Blocking eliminates the effects of aI/lurking variables.(e) The placebo effect is a concern for aI/ experimenters.

4. Which of the following sample designs does not contain a source of bias?

(a) A politician would like to know how her constituents feel about a particular issue. As a result, her office mailsquestionnaires about the issue to a random sample of adults in her political district.

(b) A company uses the telephone directory to randomly select adults for a telephone survey to gauge their feelings towarditems manufactured by the company.

(c) An interviewer selects a random sample of individuals to question about a particular issue. Since some of the individualsare not informed about the issue, the interviewer gives background and his personal view on the issue before theirresponses.

(d) A news show asks viewers to call a toll-free number to express their opinions about a recent high-publicity trial.(e) One thousand numbered tickets are sold as a fund-raiser. Five numbers are chosen randomly, and the individuals with

the winning ticket numbers each win $10.

5. A drug company wishes to test a new drug. A researcher assembles a group of volunteers and randomly assigns them toone of two groups - one to take the drug and one to take a placebo. In addition, the company wants the experiment to bedouble-blind. What is the meaning of double-blind in this situation?

(a) The volunteers in both groups are blindfolded when they take the drug or placebo.(b) The volunteers in both groups do not know whether they are taking the drug or the placebo.(c) Neither the volunteers nor the drug company executives know which volunteers are taking the drug and which are taking

the placebo.(d) Neither the volunteers nor the experimenters know which volunteers are taking the drug and which are taking the

placebo.

(e) As long as the subjects are randomly assigned to the two groups, there is no need to make the experiment double-blind.

6. Since many individuals walk around their homes in their socks, a manufacturer has created a material for socks that isbelieved to be more resistant to wear than cotton. The manufacturer wishes to test this belief over a period of a month.Given a group of volunteers, which of the following designs will best test this new material's resistance to wear?

(a) Have the volunteers wear the socks made from the new material for a month, and check the wear on the socks at theend of the month.

(b) Allow half of the volunteers to wear cotton socks, while the other half wear socks made of the new material. Comparethe wear on the socks at the end of the month.

(c) Randomly assign half of the volunteers to wear cotton socks, while the other half wear socks made of the new material.Compare the wear on the socks at the end of the month.

(d) Randomly assign half of the volunteers to wear cotton socks, while the other half wear socks made of the new material.At the end of two weeks, the volunteers should change sock types. Compare the wear on the socks at the end of themonth.

(e) For each volunteer, randomly choose which foot wears a cotton sock, while the other foot wears a sock made of the newmaterial. Compare the wear on the socks at the end of the month.

7. A university is proposing a new procedure for professors to gain tenure. It intends to randomly sample five professors,five assistant professors, five associate professors, five adjunct professors, and five visiting professors. This is an exampleof what type of sampling design?

(a) Simple random sample(b) Stratified random sample(c) Systematic random sample(d) Cluster sample(e) Convenience sample

8. A simple random sample of size n is selected in such a way that

(a) Each member of the population has an equal chance of being selected.(b) Each member of the population is given an opportunity to respond to the survey.(c) All samples of size n have the same chance of being selected.(d) The probability of selecting any sample is known to be 1/n.(e) The sample is guaranteed to represent the entire population.

9. A graduate student is conducting an experiment to determine whether a new activity-based method is better than thetraditional lecture of teaching statistics. He found two teachers to help him in his study for one semester. Mr. Dullvolunteered to continue teaching with traditional lectures and Ms. Perky agreed to try the new activity-based method. Eachteacher planned to teach two sections of approximately forty students each for adequate replication. At the end of thesemester, all sections would take the same final exam and their scores would be compared. What is the treatment variablein this study?

(a) Teacher(b) Section of the Course(c) Teaching Method(d) Final Exam Score(e) Student

10. Each person in a simple random sample of 2,000 received a survey, and 317 people returned their surveys. How couldnonresponse cause the results of the survey to be biased?

(a) Those who did not respond reduced the sample size, and small samples have more bias than large samples.(b) Those who did not respond caused a violation of the assumption of independence.(c) Those who did not respond were indistinguishable from those who did not receive the survey.(d) Those who did not respond represent a stratum, changing the simple random sample into a stratified random sample.(e) Those who did respond may differ in some important way from those who did not respond.

Part II - Free Response (Question 11-13) - Show your work and explain your results clearly.

11. Your school will send a delegation of 35 seniors to a student life convention. Two hundred girls and 150 boys areeligible to be chosen. A stratified random sample of 20 girls and 15 boys gives each senior the same chance to bechosen to attend the convention.

(a) Is this a random sample from the school? Explain your answer.

(b) Is this a simple random sample from the school? Explain your answer.

12. At a certain university, students who live in dormitories eat at a common dining hall. Recently, some students have beencomplaining about the quality of the food served there. The dining hall manager decided to do a survey to estimate theproportion of students living in the dormitories who think the quality of the food should be improved. One evening, themanager asked the first 100 students entering the dining hall to answer the following question.

Many students believe that the food served in the dining hall needs improvement. Do you think that the quality of foodserved here needs improvement, even though that would increase the cost of the meal plan?

Yes No No opinion

(a) In this setting, explain how bias may have been introduced based on the way this sample was selected and suggesthow the sample could have been selected differently to avoid that bias.

(b) In this setting, explain how bias may have been introduced based on the way the question was worded and suggesthow it could have been worded differently to avoid that bias.

13. Researchers who are studying a new shampoo formula plan to compare the condition of hair for people who use the newformula with the condition of hair for people who use the current formula. Twelve volunteers are available to participate inthis study. Information on these volunteers (numbered 1 through 12) is shown in the table below.

Volunteer GenderAge1

Male212

Female203

Male474

Female605

Female626

Male617

Male588

Female449

Male4410

Female2411

Male2312

Female46

(a) These researchers want to conduct an experiment involving the two formulas (new and current) of shampoo. Theybelieve that the condition of hair changes with age but not gender. Because researchers want the size of the blocksin an experiment to be equal to the number of treatments, they will use blocks of size 2 in their experiment. Identifythe volunteers (by number) that would be included in each of the six blocks and give the criteria you used to form theblocks.

(b) Other researchers believe that hair condition differs with both age and gender. These researchers will also useblocks of size 2 in their experiment. Identify the volunteers (by number) that would be included in each of the sixblocks and give the criteria you used to form the blocks.

(c) The researchers in part (b) decide to select three blocks to receive the new formula and to give the other threeblocks the current formula. Is this an appropriate way to assign treatments? If so, describe a method for selectingthe three blocks to receive the new formula. If not, describe an appropriate method for assigning treatments.

AP Statistics11/11/08Test #5 (Chapter 6)

Wood/MyersName 'U.D c:J?->vHonor Pledge Period ---

Part I - Multiple Choice (Questions 1-10) - Circle the letter of the answer of your choice.

1. You read in a book on poker that the probability of being dealt three of a kind in a five-card poker hand is 1/50. Whatdoes this mean?

((ci)) If you deal thousands of poker hands, the fraction of them that contain three of a kind will be very close to 1/50.W If you deal 50 poker hands, then one of them will contain three of a kind.(c) If you deal 10,000 poker hands, then 200 of them will contain three of a kind.(d) A probability of 0.02 is somebody's best guess for a probability of being dealt three of a kind.(e) It doesn't mean anything, because 1/50 is just a number.

Here is the probability model for the blood type of a randomly chosen person in the United States:

Questions 2, 3, and 4 use this information.

o0.45

A

0.40B

0.11AB?

2. The probability that a randomly chosen American has type AB blood must be(a) any number between 0 and 1.(b) 0.45.(c) 0.4.

~0.96.Ci:V 0.04.

3. Maria has type B blood. She can safely receive blood transfusions from people with blood types 0 and B. What is the

probability that a randomly chosen American can donate blood to Maria? ~(a) 0.11 (b) 0.44 (c) 0.45 (d) 0.51 ® 0.56

4. What is the probability that a randomly chosen American does not have type 0 blood?(a) 0.04(b) 0.11

(~ 0.45~0.55(e) 0.51

5. An athlete suspected of using steroids is given two tests that operate independently of each other. Test A hasprobability 0.9 of being positive if steroids have been used. Test B has probability 0.8 of being positive if steroidshave been used. What is the probability that neither test is positive if steroids have been used?(a) 0.72

(b) 0.38 ( \ \ ( 2-)@0.02 \. ) ,-.(d) 0.28(e) 0.08

6. An instant lottery game gives you probability 0.02 of winning on anyone play. Plays are independent of each other. Ifyou play 3 times, the probability that you win on none of your plays is about

fO.98.b 0.94.

c 0.000008. ( 9B)?>(d) 0.06. '(e) 0.96.

Questions 7 and 8 relate to the following: An event A will occur with probability 0.5. An event B will occur with probability

0.6. The probability that both A and B will occur is 0.1. ~ ~~ 137. The condi.ional probability o' A. given B ~(a) is 0.5.

(b) i~ 0.3. P \ A \ B') -:.. .:..l(c) IS 0.2. , lJ,

((d) is 1/6.(€i) cannot be determined from the information given.

8. We may conclude that(a) events A and B are independent.(b) events A and B are disjoint.

((CY) either A or B always occurs.(Of events A and B are complementary.(e) none of the above is correct.

9. Of people who died in the United States in a recent year, 86% were white, 12% were black, and 2% were Asian.(This ignores a small number of deaths among other races.) Diabetes caused 2.8% of deaths among whites, 4.4%among blacks, and 3.5% among Asians. The probability that a randomly chosen death is a white who died of

diabetes is about cfl!b T)(a) 0.107. <

~0.030. '01... 'W DC.c) 0.024. '/ a ~ D0.86. ~ IT""u OC

(e) 0.03784 .. o~ A ~ 1)--- DC.

10. If P(A) = 0.24 and P(B) = 0.52 and A and B are independent, what is P(A or B)?

(a) 0.1248 I l \ D{ ?>'\(b) 0.28 V(Aoyf)'Y=. 'V~A)-\() ~J- \"' An 'J

t1C)) 0.6352 ( 4'( 5'2.)la) 0.76 _ '2.q 1- ,S2- - :2- r.J I(e) The answer cannot be determined from the information given. - .

Part" - Free Response (Question 11-13) - Show your work and explain your results clearly.

11. Heart disease is the number 1 killer today. Suppose that 8% of the patients in a small town are known to have heartdisease. And suppose that a test is available that is positive in 96% of the patients with heart dis~ase, but is also positive

in 7% of patients who do not have heart disease. \-\~ 'P~t w,.S ~.I\-t ~K(;.}<'-P - -x.d'C~-' +<-~+5 1'(;I'¥1~V-<-

(a) Find the probability that a randomly selected person tests positive for heart disease. - I C\to

.:---1'O~ \ \ ~",,-7 r .Cf-\ T

~ 0' P

1'1~ \-\ c.. / c.~p,oCo¥t

• O/~B

.I~ \ 2-

~ . \~\'2

y (b) If a person is selected at random and given the test and it comes out positive, what is the probability that the personactually has heart disease?

'?(H \-p; = 'P(t-\(\'P) ~\ yf P)

12. Suppose there are 10 multiple choice questions on a quiz. Each question has five choices (a-e) for the answer.Unfortunately, you went to see a movie the night before, and you were unprepared for the quiz. You decide to guess the

correct answers by randomly choosing one of the five choices. c;:; t,DV' {.I! c..+\ 'j 0Y17>\Ne.t ~d 1lJ.O ~-h ur.(a) Describe a simulation to estimate the probability of answering at least 2 of the ten questions correctly. P(e)::. Y?

0, I-:::Lo(r~ d ().xICCWW 0Y1 ~W!s-\>OVJ

2~.::. in(..oy ( <. L-+ D...f'~w CK" (Y\ 4> \}J) <;. -i1 Gv-

\ (b) Carry out 3 repetitions of your sim ulation using Lines 1-3 of the random num ber table below.

Line I:~ 5 ~ '0 7

\' .I \

I 6632\ \ 8 I I 94148731\0419785576) 4519596565

Line 2: 6 8 7 3 2

55259842920879643 I 65937393 I 68597150

Line 3: 4 5 740

418076556 I333020705193623I 8 I 3209547

Result - Simulation #1:

~WVYtc...+0J.r.'S.N f:j. S -7~


'7 W v~+OJ ,c:",} 'JP" '5..::=r

~-./ V tResult - Simulation #3:

Z- WVYLC.tOJ 19;V"I/ O( S-=1~

13. Suppose you are given a standard six-sided die and told that the die is "loaded" in such a way that while the numbers1, 3, 4, and 6 are equally likely to turn up, the numbers 2 and 5 are three times as likely to turn up as any of the othernumbers.

\(a) The die is rolled once and the number turning up is observed. Use the information given above to fill in the

following table:

OutcomeProbabilit

1 6'/'0

\

\

(b) Let A be the event: the number rolled is a prime number (a number is prime if its only factors are 1 and thenumber itself; note that 1 is not prime). Find P(A).

'P ( A ') ~ -p l':l (?y "'J ex '? '):= ~o -\- ~o + ~o -=0 70 -= -{

(c) Let B be the event: the number rolled is an even number. Find P(B).

( ( '\ '3 \ \ SV ~') ::? 2 IX 4- ()Y <0) -= 10 t" 10 ..\. iO ~ )0 = _ t;

(d) Determine if events A and B are disjoint and explain why or why not.

V(A~ ~)-=- '\=>(IL) = 3/10=.3

~ eN'tV\~ R 6YJ b we.xe clis~U'\l, -P(f\6¥\~ I?)=O W~ ~ Yla\ ~

.:zv ~ ~~ 6.M- V1..OT ~? ~ '

\ (e) Determine if events A and B are independent and explain why or why not.

lJ('A)·t>t~)-=- ~ll\~~)

( .1 ')l .Sj:= .~

.:>~ :F.~

\-t' ~~ A OJvltl 6 ClAt'W'~~, 'P(.A),Plp':»~?(J'1~d''J)

W~ 0 '1\..0-\ ~,So ~ 0v~. \ \ W-A- O-..9.fev ~ 1.

Period _AP Statistics11/11/08Test #5 (Chapter 6)

Wood/MyersName ---::---:--:- __

Honor Pledge _


1. You read in a book on poker that the probability of being dealt three of a kind in a five-card poker hand is 1/50. Whatdoes this mean?

(a) If you deal thousands of poker hands, the fraction of them that contain three of a kind will be very close to 1/50.(b) If you deal 50 poker hands, then one of them will contain three of a kind.(c) If you deal 10,000 poker hands, then 200 of them will contain three of a kind.(d) A probability of 0.02 is somebody's best guess for a probability of being dealt three of a kind.(e) It doesn't mean anything, because 1/50 is just a number.

Here is the probability model for the blood type of a randomly chosen person in the United States:

Questions 2, 3, and 4 use this information.

o0.45

A

0.40B

0.11AB?

2. The probability that a randomly chosen American has type AB blood must be(a) any number between 0 and 1.(b) 0.45.(c) 0.4.(d) 0.96.(e) 0.04.

3. Maria has type B blood. She can safely receive blood transfusions from people with blood types 0 and B. What is theprobability that a randomly chosen American can donate blood to Maria?(a) 0.11 (b) 0.44 (c) 0.45 (d) 0.51 (e) 0.56

4. What is the probability that a randomly chosen American does not have type 0 blood?(a) 0.04(b) 0.11(c) 0.45(d) 0.55(e) 0.51

5. An athlete suspected of using steroids is given two tests that operate independently of each other. Test A hasprobability 0.9 of being positive if steroids have been used. Test B has probability 0.8 of being positive if steroidshave been used. What is the probability that neither test is positive if steroids have been used?(a) 0.72(b) 0.38(c) 0.02(d) 0.28(e) 0.08

6. An instant lottery game gives you probability 0.02 of winning on anyone play. Plays are independent of each other. Ifyou play 3 times, the probability that you win on none of your plays is about(a) 0.98.(b) 0.94.(c) 0.000008.(d) 0.06.(e) 0.96.

Questions 7 and 8 relate to the following: An event A will occur with probability 0.5. An event B will occur with probability0.6. The probability that both A and B will occur is 0.1.

7. The conditional probability of A, given B(a) is 0.5.(b) is 0.3.(c) is 0.2.(d) is 1/6.(e) cannot be determined from the information given.

8. We may conclude that(a) events A and B are independent.(b) events A and B are disjoint.(c) either A or B always occurs.(d) events A and B are complementary.(e) none of the above is correct.

9. Of people who died in the United States in a recent year, 86% were white, 12% were black, and 2% were Asian.(This ignores a small number of deaths among other races.) Diabetes caused 2.8% of deaths among whites, 4.4%among blacks, and 3.5% among Asians. The probability that a randomly chosen death is a white who died ofdiabetes is about(a) 0.107.(b) 0.030.(c) 0.024.(d) 0.86.(e) 0.03784.

10. If P(A) = 0.24 and P(B) = 0.52 and A and B are independent, what is P(A or B)?(a) 0.1248(b) 0.28(c) 0.6352(d) 0.76(e) The answer cannot be determined from the information given.


11. Heart disease is the number 1 killer today. Suppose that 8% of the patients in a small town are known to have heartdisease. And suppose that a test is available that is positive in 96% of the patients with heart disease, but is also positivein 7% of patients who do not have heart disease.

(a) Find the probability that a randomly selected person tests positive for heart disease.

(b) If a person is selected at random and given the test and it comes out positive, what is the probability that the personactually has heart disease?

12. Suppose there are 10 multiple choice questions on a quiz. Each question has five choices (a-e) for the answer.Unfortunately, you went to see a movie the night before, and you were unprepared for the quiz. You decide to guess thecorrect answers by randomly choosing one of the five choices.

(a) Describe a simulation to estimate the probability of answering at least 2 of the ten questions correctly.

(b) Carry out 3 repetitions of your simulation using Lines 1-3 of the random number table below.

Line I: 0 5 0 0 7 I66328 I 1941487304197855764519596565

Line 2: 6 8 7 3 2

55259842920879643165937393 I 68597150

Line 3: 4 5 7 4 0

41807655613330207051936231813209547


Result - Simulation #2:Result - Simulation #3:

13. Suppose you are given a standard six-sided die and told that the die is "loaded" in such a way that while the numbers1, 3, 4, and 6 are equally likely to turn up, the numbers 2 and 5 are three times as likely to turn up as any of the othernumbers.

(a) The die is rolled once and the number turning up is observed. Use the information given above to fill in thefollowing table:

Outcome

Probability

1 2 3 4 5 6

(b) Let A be the event: the number rolled is a prime number (a number is prime if its only factors are 1 and thenumber itself; note that 1 is not prime). Find P(A).

(c) Let B be the event: the number rolled is an even number. Find P(B).

(d) Determine if events A and B are disjoint and explain why or why not.

(e) Determine if events A and B are independent and explain why or why not.

Honor Pledge _

*\~Part I - Multiple Choice (Questions 1-10) - Circle the letter of the answer of your choice.

AP Statistics

11/20/08 Wood/MyersTest #6 (Chapter 7)

NamePeriod ---

1. A random variable is:

(a) a hypothetical list of possible outcomes of a random phenomenon.(b) any phenomenon in which outcomes are equally likely.

~c any number that changes in a predictable way in the long run.a) variable whose value is a numerical outcome of a random phenomenon.

one of the above.

Questions 2 and 3 refer to the following information.Use the following information for questions 7-9. The independent random variables X and Yare defined by the followingprobability distribution tables.

xP(X)

1.6

3.3

6.1

Y

P(Y)

2.1

3.2

5.3

7.4

2. Determine the mean of X+Y

~7.2I.....'to"). 8.4(c) 5.1(d) 9(e) 4.3

3. Determine the standard deviation of 4X - 5Y.

(a) 15.38 04X-Sy::: ~-4-'7i-'2-'J.-+-S-215-2--y:: J 17-?-, 0 '1

f-2.76(c 11.05a) 10.62

(e) cannot be determined from the given information

4. Which of the following is not true concerning discrete probability distributions?

(a) The probability of any specific value is between 0 and 1, inclusive.(b) The mean of the distribution is between the smallest and largest value in the distribution.

~ The sum of all probabilities is 1.@))The standard deviation of the distribution is between -1 and 1.(e) The distribution may be displayed using a probability histogram.

5. A random variable X has a probability distribution as follows:X 0 1 2 3

P(X) 2k 3k 13k 2k

Then the probability that P(X < 2.0) is equal to(a) 0.90.

((D))0.25.1cJ 0.65.(d) 0.15.(e) 1.00.

E ('j) == • 30 ~ LX')

Vcor(y') ~ • 3DzVcu{~)

6. Cans of soft drinks cost $ 0.30 in a certain vending machine. What is the expected value and variance of daily revenue(Y) from the machine, if X, the number of cans sold per day hasE(X) = 125, and Var(X) = 50 ?

fa E(Y) = 37.5, Var(Y) = 50b) E(Y) = 37.5, Var(Y) = 4.5c E(Y) = 37.5, Var(Y) = 15

(d) E(Y) = 37.5, Var(Y) = 30(e) E(Y) = 125, Var(Y) = 4.5

7. An insurance company has estimated the following cost probabilities for the next year on a particular model of car:

The expected cost to the insurance company is (approximately)

~ $155.~$595.(c) $875.(d) $645.(e) $495.

8. Suppose X is a continuous random variable taking values between a and 2 andhaving the probability density function below.

P(1 ::; X ::;2) has value(a) , 0.50.(b) 0.33.

(lCb0.25.(aT 0.00.(e) None of these.

o

o 2

Questions 9 and 10 relate to the following information.The weight of medium-size oranges selected at random from a bin at the local supermarket is a random variable withmean Jl = 10 ounces and standard deviation (J" = 1 ounce.

9. Suppose we pick two oranges at random from the bin. The difference in the weights of the two oranges selected (the

weight of the first orange minus the weight of the second ora~~ is a random variable with a mean (in ounces) of(a) 10. (b) 1. (c) 1.41. ®O. (e) 5.

10. Suppose we pick two oranges at random from the bin. The difference in the weights of the two oranges selected (theweight of the first orange minus the weight of the second orange) is a random variable with a standard deviation (inounces) of

(a) O. (b) 1. (c) 2. (d) 2.2. ® .41.


1-- 11. AP Statistics test scores on Random Variables are described by the following probability distribution.

I Score I 70 I 80 IP(Score) .4 .6

Set up the probability distribution for the random variables:

(a) Score + Score. (b) 2 * Score

~I . Co

v ~ s -Wv- yv\Clc.lu.MJ ~ \P-- -t"¥vr-0

\.M~~'(V""\) MCL~ 'b \'S

D&-()J{ ~~c.+ (.• \\0\ 0

A- 12. A department supervisor is considering purchasing one of two comparable photocopy machines, A or B. Machine A~\ costs $10,000 and machine B costs $10,500. This department replaces photocopy machines every three years. Therepair contract for machine A costs $50 per month and covers an unlimited number of repairs. The repair contract for

'lJP \ machine B costs $200 per repair. Based on past performance, the distribution of the number of repairs needed over any

~ '}... one-year period for machine B is shown below:

Number of RepairsProbabilit

You are asked to give a recommendation based on overall cost as to which machine, A or B, along with its repair contract,should be purchased. What would be your recommendation be? Give a statistical justification to support yourrecom mendation.

A :::.\0000 -t 50 (~(0 '):::. \ \ ~o 0

t>::: \0000 + 200 (2 .CSS") :: \ \ 0 \ D

~ Dv\f€Ji ~ ~A:..{ ~

\.Af,O\<; VJ 2:5'5. &\'Ve/) ~

4; 1C) 0 C.-\;\JL~ ~ ~ --thY'u....

\jQJ\~ ~ \\'600 ).

J\ 13. Two antibiotics are available as treatment for a common ear infection in children.

•\ • Antibiotic A is known to effectively cure the infection 60 percent of the time.7JP'1 costs $50.~t.\ · Antibiotic B is known to effectively cure the infection 90 percent of the time.costs $80.

Treatment with antibiotic A

Treatment with antibiotic-g '6

••

The antibiotics work independently of one another. Both antibiotics can be safely administered to children. A healthinsurance company intends to recommend one of the following two plans of treatment for children with this ear infection.

Plan I: Treat with antibiotic A first. If it is not effective, then treat with antibiotic B. 1+- A- I ~ e-f.R:c:hVc

Plan II: Treat with antibiotic B first. If it is not effective, then treat with antibiotic A. 1J.- _ (1r_ ",J:.... .u-=:- 13 I> CL:i"i""C-~ \ VC

(a) If a doctor treats a child with an ear infection using Plan I, what is the probability that the child will be cured?

y lA l5Y Bn A C ")::: l~00") + (·q0)( ..40) :: . 4 Co

If a doctor treats a child with an ear infection using Plan II, what is the probability that the child will be cured?

?( B OY F\,,~~)::= (.CJO) + (,(po)(..\D) ::: ,C1lo

(b) Compute the expected cost per child when plan I is used for treatment.

~± ~50 T~J~D- r-- ---- £(C£Xct-)::: ~ B 7-?(W~{)\ .00 .4D

Compute the expected cost per child when plan II is used for treatment.

(c) Based on the results in parts (a) and (b), which plan would you recommend?Explain your recommendation.

~'\U ct\M ~~ t OM ~ ~ .)J

~ ~ cJ;:.N. jJAJt> ~» --.r ~ £l ~-t -Ltu.

~ Db:t..1N2 ~ pL!L v\/l- \N~ ~ pl~ \ ..

AP'"STATISTICS2001 SOLUTIONS AND SCORING GUIDELINES

Question 2 - Solution

For A:

Total 3-year cost:This cost is fixed.

For B:

$10,000 + 36($50) = $10,000 + $1,800 = $11,800

Expected number of repairs in 3 years = 3[0(.5) + 1(.25) + 2(.15) + 3(.1)] = 3(.85) = 2.55Expected cost of repairs in 3 years = 3($200)(0.85) = $510Expected 3-year cost = $10,500 + $510 = $11,0 10

Choice:

Choose B because it has a lower expected (or average) cost. (A has a fixed cost that is $790 ($11,800 $11,0 I0) higher than the expected cost of B.)

Scoring

The solution should include the following four elements:

I. Correct calculation of 3-year cost for A.2. Correct calculation of a relevant expected value for B (expected number of repairs per year or per

3 years or expected cost of repairs per year or per 3 years). Calculation of expected value must beshown.

3. Correct calculation of expected total cost for B.4. Choice of B with a complete and coherent explanation that is based on student's prior calculations

for A & B.

"Complete and coherent" means that:• costs for A & B are comparedAND

• B's cost has been indicated as "expected" or "average" or "mean" or "estimated" or"approximate" or "predicted," etc.

4 Complete ResponseSolution includes all four of the required elements.

3 Substantial ResponseSolution includes three of the required elements.

2 Developing ResponseSolution includes two of the required elements.

1 Minimal ResponseSolution includes one of the required elements.

Copyright © 2001 by College Entrance Examination Board. All rights reserved.Advanced Placement Program and AP are registered trademarks of the College Entrance Examination Board.

4

AP@STATISTICS2001 SOLUTIONS AND SCORING GUIDELINES

Question 2 (cont'd.)

Notes:

I. If calculations are based on I-year costs rather than 3-year costs, and then the student chooses A withexplanation, the student can earn a score of up to 3.

Total I-year cost for A: $10,000 + 12($50) = $10,000 + $600 = $10,600And for B:

Expected number of repairs in I year = 0(.5) + 1(.25) + 2(.15) + 3(.1) = .85Expected cost of repairs in I year = $0(.5) + $200(.25) + $400(.15) + $600(.1) = $170Expected I-year cost for B: $10,500 + $170 = $10,670

2. If initial purchase prices are omitted from the calculations, the student can earn a score of up to 3.

3. Rounded calculations_of the expected number of repairs for B: Ifa student rounds the expectednumber of repairs per year (.85) to I, or rounds the expected number of repairs in 3 years (2.55) to 3,the maximum score is a 3. If the student identifies the rounded value as an upper bound on theexpected cost, the paper may earn a maximum score of 4.

4. If choice of A or B is not based on expected cost for B, the student can still present a completeresponse. To earn 4 points with this solution, relevant and complete statistical reasoning must bedemonstrated. This solution must include:

a. Decision based on break-even analysis:

I point -- Correct calculation of 3-year fixed cost for A ($11,800)

I point -- Correct calculation that 7 or more repairs in the 3-year period would be necessary forB's cost to exceed A's 3-year cost

I point -- Says or calculates that the probability of 7 or more repairs for B is small and thereforechooses B,

ORChooses A because the probability of 7 or more repairs for B is not 0 and they want toguard against the possibility of paying more for B than A's fixed cost

I point -- Correctly calculates that the probability of 7 or more repairs for B is 0.0 1975 (or about0.02, or about 2 percent of the time B's cost will exceed A's cost)

AND

States that this analysis depends on the assumption that repairs from year to year areindependent

Copyright © 200 I by College Entrance Examination Board. All rights reserved.Advanced Placement Program and AP are registered trademarks of the College Entrance Examination Board.

5

AP@STATISTICS2001 SOLUTIONS AND SCORING GUIDELINES

Question 2 (cont' d.)

b. Decision based on minimax analysis may earn a maximum of 3 points:

I point -- Correct calculation of 3-year fixed cost for A ($11,800)

I point -- Correct calculation of range of possible 3-year costs for B$10,500:::: cost of B ::::$12,300

AND

Probability calculation showing that chance of observing maximum cost is small(e.g., 0.00 I or 0.1 percent that B costs $12,500, assuming independence)

I point -- Relevant statistical justification for choice of A or B:

Gives convincing reasoning for minimizing maximum cost (minimax) and therefore chooses A. Studentmight argue, for example, that a company may prefer a known fixed cost to a variable cost that could besmaller but also has the chance of being larger.

Copyright © 2001 by College Entrance Examination Board. All rights reserved.Advanced Placement Program and AP are registered trademarks of the College Entrance Examination Board.

6

Ap® STATISTICS2004 SCORING GUIDELINES

Question 4

Solution

Part (a):

Let A be the event "antibiotic A works."Let B be the event "antibiotic B works."

The probability that a child will be cured with Plan I is:

P( Cure,)= p( A) + p( not A) P(B)

= 0.6 + (0.4 x 0.9)

= 0.96

The probability that a child will be cured with Plan II is:

P(Curen)=P(B) +p(notB)P(A)

= 0.9 + (0.1 x 0.6)= 0.96

Part(b):

Treatment with antibiotic A costs $50, and treatment with antibiotic B costs $80.

The expected cost per child when Plan I is used for treatment is:

E (Cost,) = $50x 0.6 + $130x 0.4

= $30+$52

=$82

The expected cost per child when Plan II is used for treatment is:

E (Costn) = $80xO.9+ $130x 0.1

=$72+$13

=$85

Part (c):

Since the probability that a child will be cured is the same under either plan, some other criterion must be usedto make a recommendation. From a financial point of view, Plan I should be recommended because theexpected cost per child is less than Plan II.

Copyright © 2004 by College Entrance Examination Board. All rights reserved.

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17



Scoring

Each part is scored as essentially correct, partially correct, or incorrect.

Part (a) is essentially correct if the probabilities of cure are calculated correctly with justification for both plans.

Plan I:

<I A works (0.6) I

I A doesn't work (0.4)

I B works (0.9) I]< B doesn't work (0.1)

Plan II:

P( Curel) = 0.6 + (0.4 x 0.9) = 0.96

OR

P(CureI)=P(A u B) =0.6+0.9-(0.6xO.9)=0.96

OR

P(Curel)= I - p( not A)P(not B) = I - (0.4) x (0.1) = 0.96

<I B works (0.9) I

I B doesn't work (0.1)

IA works (0.6) I]< A doesn't work (0.4)

P( Cure II ) = 0.9 + (0.1 x 0.6) = 0.96

OR

P(Curell)= P(B u A) = 0.9 + 0.6 - (0.9 x 0.6) = 0.96

OR

P(Curell)= I-P(notB)P(notA) = 1-(0.1) x (0.4)=0.96


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13



Part (a) is partially correct if

one of the two probabilities is calculated correctly with justification,

OR

both probabilities are correct with incomplete justifications.

Part (b) is essentially correct if the expected costs per child are calculated correctly with justification for both plans.


E (Cost,) = $50x 0.6 + $130x 0.4

= $30+ $52

=$82

OR

E(Costr) = $50+0.4x$80

= $50+$32

=$82


E(Costn) = $80xO.9+$130xO.l

= $72+$13

=$85

OR

E (Costn ) = $80+0. I X $50

= $80+$5

=$85

Part (b) is partially correct ifthe expected cost per child is calculated correctly with justification for one of the two plans,

OR

both expected costs are correct with incomplete justifications,

OR

the expected costs are incorrectly calculated but the probabilities involved add up to I. For example thefollowing computations would receive a partial.


= $50xO.6 +$80x0.4 = $30 +$32 = $62


= $80xO.9 + $50xO. 1= $72 + $5 = $77


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In contrast, the following computations would receive an incorrect because the probabilities involved do notadd up to 1.


= $50xO.6 + $130xO.36 = $30 + $46.80 = $76.80


= $80xO.9+$130xO.06 = $72+$7.80 = $79.80

Part (c) is essentially correct if the recommendation contains a statistical argument based on parts (a) and (b). That is,the student must base the recommendation on probabilities from part (a) and expected values from part (b). Thefollowing two examples are essentially correct:

Since the probability that a child will be cured is the same under either plan, some other criterion must be usedto make a recommendation. From a financial point of view, Plan I should be recommended because theexpected cost per child is less than Plan II.

Since the probability that a child will be cured is the same under either plan, some other criterion must be usedto make a recommendation. Parents might prefer Plan II, regardless of its higher cost, because their child ismore likely to need only the first drug.

Part (c) is partially correct if the recommendation contains a statistical argument based only on part (a) or (b) but notboth.

Part (c) is incorrect if no recommendation is made.


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15



4 Complete Response

All three parts essentially correct

3 Substantial Response

Two parts essentially correct and 1 part partially correct

2 Developing Response

Two parts essentially correct and no parts partially correct

OR

One part essentially correct and 2 parts partially correct

OR

1

Three parts partially correct

Minimal Response

One part essentially correct and either 0 or 1 part partially correct

OR

No parts essentially correct and 2 parts partially correct

..--


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AP Statistics11/20/08Test #6 (Chapter 7)

Wood/MyersName _

Period _Honor Pledge _


1. A random variable is:

(a) a hypothetical list of possible outcomes of a random phenomenon.(b) any phenomenon in which outcomes are equally likely.(c) any number that changes in a predictable way in the long run.(d) a variable whose value is a numerical outcome of a random phenomenon.(e) None of the above.

Questions 2 and 3 refer to the following information.Use the following information for questions 7-9. The independent random variables X and Yare defined by the followingprobability distribution tables.

xP(X)

1.6

3.3

6.1

ypm

2.1

3.2

5.3

7.4

2. Determine the mean of X+Y

(a) 7.2(b) 8.4(c) 5.1(d) 9(e) 4.3

3. Determine the standard deviation of 4X - 5Y.

(a) 15.38(b) -2.76(c) 11.05(d) 10.62(e) cannot be determined from the given information

4. Which of the following is not true concerning discrete probability distributions?

(a) The probability of any specific value is between 0 and 1, inclusive.(b) The mean of the distribution is between the smallest and largest value in the distribution.(c) The sum of all probabilities is 1.(d) The standard deviation of the distribution is between -1 and 1.(e) The distribution may be displayed using a probability histogram.

5. A random variable X has a probability distribution as follows:X 0 1 2 3

P(X) 2k 3k 13k 2k

Then the probability that P(X < 2.0) is equal to(a) 0.90.(b) 0.25.(c) 0.65.(d) 0.15.(e) 1.00.

6. Cans of soft drinks cost $ 0.30 in a certain vending machine. What is the expected value and variance of daily revenue(Y) from the machine, if X, the number of cans sold per day hasE(X) = 125, and Var(X) = 50 ?(a) E(Y) = 37.5, Var(Y) = 50(b) E(Y) = 37.5, Var(Y) = 4.5(c) E(Y) =37.5, Var(Y) = 15(d) E(Y) = 37.5, Var(Y) = 30(e) E(Y) = 125, Var(Y) = 4.5

7. An insurance company has estimated the following cost probabilities for the next year on a particular model of car:

The expected cost to the insurance company is (approximately)(a) $155.(b) $595.(c) $875.(d) $645.(e) $495.

8. Suppose X is a continuous random variable taking values between a and 2 andhaving the probability density function below.

P(1 ::; X ::;2) has value(a) 0.50.(b) 0.33.(c) 0.25.(d) 0.00.(e) None of these.

o

o 2

Questions 9 and 10 relate to the following information.The weight of medium-size oranges selected at random from a bin at the local supermarket is a random variable withmean J.1 = 10 ounces and standard deviation iT = 1 ounce.

9. Suppose we pick two oranges at random from the bin. The difference in the weights of the two oranges selected (theweight of the first orange minus the weight of the second orange) is a random variable with a mean (in ounces) of(a) 10. (b) 1. (c) 1.41. (d) O. (e) 5.

10. Suppose we pick two oranges at random from the bin. The difference in the weights of the two oranges selected (theweight of the first orange minus the weight of the second orange) is a random variable with a standard deviation (inounces) of(a) O. (b) 1. (c) 2. (d) 2.2. (e) 1.41.

Part 11- Free Response (Question 11-13) - Show your work and explain your results clearly.

11. AP Statistics test scores on Random Variables are described by the following probability distribution.

I Score I 70 I 80 IP(Score) .4 .6

Set up the probability distribution for the random variables:

(a) Score + Score. (b) 2 * Score

12. A department supervisor is considering purchasing one of two comparable photocopy machines, A or B. Machine Acosts $10,000 and machine B costs $10,500. This department replaces photocopy machines every three years. Therepair contract for machine A costs $50 per month and covers an unlimited number of repairs. The repair contract formachine B costs $200 per repair. Based on past performance, the distribution of the number of repairs needed over anyone-year period for machine B is shown below:

You are asked to give a recommendation based on overall cost as to which machine, A or B, along with its repair contract,should be purchased. What would be your recommendation be? Give a statistical justification to support yourrecommendation.

13. Two antibiotics are available as treatment for a common ear infection in children.

•

•

Antibiotic A is known to effectively cure the infection 60 percent of the time. Treatment with antibiotic Acosts $50.Antibiotic B is known to effectively cure the infection 90 percent of the time. Treatment with antibiotic Acosts $80.

The antibiotics work independently of one another. Both antibiotics can be safely administered to children. A healthinsurance company intends to recommend one of the following two plans of treatment for children with this ear infection.

• Plan I: Treat with antibiotic A first. If it is not effective, then treat with antibiotic B.• Plan II: Treat with antibiotic B first. If it is not effective, then treat with antibiotic A.

(a) If a doctor treats a child with an ear infection using Plan I, what is the probability that the child will be cured?

If a doctor treats a child with an ear infection using Plan II, what is the probability that the child will be cured?

(b) Compute the expected cost per child when plan I is used for treatment.

Compute the expected cost per child when plan II is used for treatment.

(c) Based on the results in parts (a) and (b), which plan would you recommend?Explain your recommendation.

AP Statistics12/9/08 Wood/MyersTest #7 (Chapter 2)

Name ri)'; {fAJ '--'

Honor Pledge Period---


1. The heights of American men aged 18 to 24 are approximately normally distributed with mean 68 inches and standarddeviation 2.5 inches. Half of all young men are shorter than

~ 65.5 inches@D68inches(c) 70.5 inches(d) can't tell, because the median height is not given(e) none of the above

2. Use the information in the previous problem. Only about 5% of young men have heights outside the range

Jat 65.5 inches to 70.5 inchesC£.22) 63 inches to 73 inches(c) 60.5 inches to 75.5 inches(d) 58 inches to 78 inches(e) none of the above

3. The area under the standard Normal curve corresponding to -0.3 < Z < 1.6 is(a) 0.3273(b) 0.4713

((C)9·5631~0.9542(e) none of the above

4. In some courses (but certainly not in an intro stats course!), students are graded on a "Normal curve." For example,students within ± 0.5 standard deviations of the mean receive a C; between 0.5 and 1.0 standard deviations above themean receive a C+; between 1.0 and 1.5 standard deviations above the mean receive a B; between 1.5 and 2.0standard deviations above the mean receive a B+, etc. The class average on an exam was 60 with a standarddeviation of 10. The bounds for a B grade and the percent of students who will receive a B grade if the marks areactually Normally distributed are(a) (65, 75), 24.17%

1I2l(70, 75), 18.38%~'(70, 75), 9.19%(d) (65,75),12.08%(e) (70, 75), 6.68%

5. The plot shown at the right is a Normal probability plot for a set of data. The data value isplotted on the x axis, and the standardized value is plotted on the yaxis. Which statementis true for these data?

(a) The data are clearly normally distributed.(b) The data are approximately normally distributed.

(sl The data are clearly skewed to the left.d9Y The data are clearly skewed to the right.(e) There is insufficient information to determine the shape of the distribution.

~ A normal density curve has which of the following properties?(a) It is symmetric.(b) It has a peak centered above its mean.

~ The spread of the curve is proportional to it's standard deviation.~ All of the properties (a) to (c) are correct.(e) None of the properties (a) to (c) is correct.

F"1:LIaa

(e) All of (a) through (d)

7. If a store runs out of advertised material during a sale, customers become upset, and the store loses not only the salebut also goodwill. From past experience, a music store finds that the mean number of CDs sold in a sale is 845, thevariance is 225, and a histogram of the demand is approximately normal. The manager is willing to accept a 2.5%

chance that a CD will be sold out. About how many CDs sho~he manager order for an upcoming sale?(a) 1295 (b) 1070 (c) 935 ~875 (e) 860

8. The yield of a variety of wheat was measured on a series of small plots and was found to be approximately normal.The 2nd and 98th percentile were found to be 29 bushels/acre and 41 bushels/acre respectively. The standard

deviation (bushels/acre) is approximately C§) -2 r::h 'J-q - ~S(a) 12 (b) 6 (c) 4 (d (e) 2 r ~ ~ f5

9. Which of the following histograms would be best approximated bY~Ormal distribution?(a) (b) (c)

p." ~ "'''~ ' , ,1"1'1'1-1 1"1;1'1=:1:0l"1~x-<:1: 1'1=:<: I"1(1XO~.:1:

(d) F'1:L1

1"1;1'1=0l"1(1x<1 I'I=:<:~

10. Which of the following is (are) a true statement?I.The area under a Normal curve is always 1, regardless of the mean and standard deviation.

II.The mean is always equal to the median for any Normal distribution.III.The interquartile range for any Normal curve extends from J-i -10- to J-i + 10- .

rWJl and II~Iandlll(c) II and III(d) I, II, and III(e) None of the above gives the correct set of true statements.

A

Part 11- Free Response (Question 11-13) - Show your work and explain your results clearly.

t:\ 11. The heights of NCAA women basketball players are approximately normally distributed with J.1 = 70 and CY = 2.5 .For each of the following, illustrate with a picture and evaluate.

(a) P(Height > 66)

lo~ 10

(c) P(Height < 64)

(P'T 70

(b) P(72 :<:; Height :<:; 74)

(d) The value of X if P(Height > X) = 0.215.

10 X

olSl1

? 12. ACT scores for the 1,171,460 members of the 2004 high school graduating class who took the test closely followedthe Normal distribution with mean 20.9 and standard deviation 4.8. Two students are chosen independently and at

random from this group. M X DJJ..J.. ~ \?l. iW 0 ~~1.n ~Y2.- (a) What is the expected sum of their scores?

V 'lJb) What is the expected difference of their scores?

M'1--Md=- 0\ (c) What is the standard deviation of the difference in their scores?

~.106

\ (d) Find the probability~t the sum of their scores is greater than 50.

T (SUM t;f $cuves '>50):: . l \ 3S

3 13. A commuter airline uses 18-seat turbo-prop airplanes and it is important that the total weight of passengers and theirbags does not exceed limits for safe take-off weight. It is know that the weights of passengers and their baggage areapproximately normally distributed with the following means and standard deviations. Assume the weights of apassenger and his or her baggage are independent, and that these weights are independent from passenger topassenger.

Mean Standard Deviation175 2570 13

po-s~~~ W~<V ••

1- W<A~~""'1-Wb'f 1(a) What are the mean and standard deviation for the combined weight of a passenger and a passenger's baggage?

;LlT-=- \-,S~-,O-=- ;2.4S

DT :: ~ 2..S2+,~ '2- -:. '25. \5

2.. (b) The allowed maximum weight of all passengers and their baggage ~ 4700 pounds. What is the probability that afull flight of 18 passengers and their baggage will overload the aircraft?

F:::-T-+T+T-t ... -rT'--- -----y--=- \ B .245 ~ 4-?\\O

fI0(2-B.10)2.:::.. 1/9.55

1<0

, OO-'Co

AP Statistics

12/9/08 Wood/MyersTest #7 (Chapter 2)

Name ----------------------Period _

Honor Pledge _


1. The heights of American men aged 18 to 24 are approximately normally distributed with mean 68 inches and standarddeviation 2.5 inches. Half of all young men are shorter than(a) 65.5 inches(b) 68 inches(c) 70.5 inches(d) can't tell, because the median height is not given(e) none of the above

2. Use the information in the previous problem. Only about 5% of young men have heights outside the range(a) 65.5 inches to 70.5 inches(b) 63 inches to 73 inches(c) 60.5 inches to 75.5 inches(d) 58 inches to 78 inches(e) none of the above

3. The area under the standard Normal curve corresponding to -0.3 < Z < 1.6 is(a) 0.3273(b) 0.4713(c) 0.5631(d) 0.9542(e) none of the above

4. In some courses (but certainly not in an intro stats course!), students are graded on a "Normal curve." For example,students within ± 0.5 standard deviations of the mean receive a C; between 0.5 and 1.0 standard deviations above themean receive a C+; between 1.0 and 1.5 standard deviations above the mean receive a B; between 1.5 and 2.0standard deviations above the mean receive a B+, etc. The class average on an exam was 60 with a standarddeviation of 10. The bounds for a B grade and the percent of students who will receive a B grade if the marks areactually Normally distributed are(a) (65, 75), 24.17%(b) (70, 75), 18.38%(c) (70, 75), 9.19%(d) (65,75), 12.08%(e) (70, 75), 6.68%

5. The plot shown at the right is a Normal probability plot for a set of data. The data value isplotted on the x axis, and the standardized value is plotted on the yaxis. Which statementis true for these data?(a) The data are clearly normally distributed.(b) The data are approximately normally distributed.(c) The data are clearly skewed to the left.(d) The data are clearly skewed to the right.(e) There is insufficient information to determine the shape of the distribution.

6. A normal density curve has which of the following properties?(a) It is symmetric.(b) It has a peak centered above its mean.(c) The spread of the curve is proportional to it's standard deviation.(d) All of the properties (a) to (c) are correct.(e) None of the properties (a) to (c) is correct.

~ 1:L 1

a

aa

7. If a store runs out of advertised material during a sale, customers become upset, and the store loses not only the salebut also goodwill. From past experience, a music store finds that the mean number of CDs sold in a sale is 845, thevariance is 225, and a histogram of the demand is approximately normal. The manager is willing to accept a 2.5%chance that a CD will be sold out. About how many CDs should the manager order for an upcoming sale?(a) 1295 (b) 1070 (c) 935 (d) 875 (e) 860

8. The yield of a variety of wheat was measured on a series of small plots and was found to be approximately normal.The 2nd and 98th percentile were found to be 29 bushels/acre and 41 bushels/acre respectively. The standarddeviation (bushels/acre) is approximately(a) 12 (b) 6 (c) 4 (d) 3 (e) 2

9. Which of the following histograms would be best approximated by a normal distribution?(a) (b) (c)

f 1:L 1

•.•.•il'l=1•.•.•ax(<: 1'1=<:

(d) F'1:L1

•.•.•il'l=O•.•.•ax(1 1'1=<:3

•.•.•;1'1=<:0•.•.•ax(33.<: 1'1=7

(e) All of (a) through (d)

F'1:L1

10. Which of the following is (are) a true statement?I.The area under a Normal curve is always 1, regardless of the mean and standard deviation.

II.The mean is always equal to the median for any Normal distribution.

III.The interquartile range for any Normal curve extends from Ji -1(J" to Ji + 1(J" .

(a) I and II(b) I and III(c) II and III(d) I, II, and III(e) None of the above gives the correct set of true statements.


11. The heights of NCAA women basketball players are approximately normally distributed with J.1 = 70 and (5 = 2.5 .For each of the following, illustrate with a picture and evaluate.

(a) P(Height > 66)

(c) P(Height < 64)

(b) P(72 ~ Height ~ 74)

(d) The value of X if P(Height > X) = 0.215.

12. ACT scores for the 1,171,460 members of the 2004 high school graduating class who took the test closely followedthe Normal distribution with mean 20.9 and standard deviation 4.8. Two students are chosen independently and atrandom from this group.

(a) What is the expected sum of their scores?

(b) What is the expected difference of their scores?

(c) What is the standard deviation of the difference in their scores?

(d) Find the probability that the sum of their scores is greater than 50.

13. A commuter airline uses 18-seat turbo-prop airplanes and it is important that the total weight of passengers and theirbags does not exceed limits for safe take-off weight. It is know that the weights of passengers and their baggage areapproximately normally distributed with the following means and standard deviations. Assume the weights of apassenger and his or her baggage are independent, and that these weights are independent from passenger topassenger.

Mean17570

Standard Deviation2513

(a) What are the mean and standard deviation for the combined weight of a passenger and a passenger's baggage?

(b) The allowed maximum weight of all passengers and their baggage i3 4700 pounds. What is the probability that afull flight of 18 passengers and their baggage will overload the aircraft?

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