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a) 0.54

b) 0.12

c) 0.58

d) 0.70

e) 0.51

f) None of the above.

Question 4

Given the following sampling distribution:

X -17 -12 2 11 15

P(X) 7⁄1001⁄20

1⁄1003⁄50 ___

What is P(X = 15)?

a) 0.82

b) 0.81

c) 0.80

d) 0.15

e) 0.79

f) None of the above

Question 5

Given the following sampling distribution:

X -16 -11 -3 11 16

P(X) 1⁄203⁄100

1⁄209⁄100 ___

What is P(X > -11)?

a) 0.95

b) 0.92

c) 0.94

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d) 0.90

e) 0.91

f) None of the above

Question 6

Given the following sampling distribution:

X -18 -10 -4 11 15

P(X) 3⁄1003⁄100

9⁄1003⁄100 ___

What is the mean of this sampling distribution?

a) -1.2

b) 11.2

c) 11.4

d) 11.1

e) -0.4

f) None of the above

Question 7

Suppose you have a distribution, X, with mean = 13 and standard deviation = 3. Define a new randomvariable Y = 4X - 5. Find the mean and standard deviation of Y.

a) E[Y] = 47; σY = 7

b) E[Y] = 47; σY = 48

c) E[Y] = 47; σY = 12

d) E[Y] = 52; σY = 7

e) E[Y] = 52; σY = 48

f) None of the above

Question 8

In testing a certain kind of missile, target accuracy is measured by the average distance X (from the target) atwhich the missile explodes. The distance X is measured in miles and the sampling distribution of X is given

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by:

X 0 10 50 100

P(X) 1⁄141⁄7 2⁄7 1⁄2

Calculate the mean of this sampling distribution.

a) 37.6

b) 64.2

c) 65.7

d) 1410.2

e) 67.2

f) None of the above

Question 9

In testing a certain kind of missile, target accuracy is measured by the average distance X (from the target) atwhich the missile explodes. The distance X is measured in miles and the sampling distribution of X is givenby:

X 0 10 50 100

P(X) 1⁄321⁄16

1⁄8 25⁄32

Calculate the variance of this sampling distribution.

a) 906.3

b) 302.1

c) 85.0

d) 30.1

e) 4766.7

f) None of the above

Question 10

Suppose you want to play a carnival game that costs 5 dollars each time you play. If you win, you get $100.The probability of winning is 3⁄100. What is the expected value of the amount the carnival stands to gain?

a) 2.00

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b) 3.00

c) 2.20

d) 2.30

e) -2.00

f) None of the above

Question 11

Suppose you want to play a carnival game that costs 5 dollars each time you play. If you win, you get $100.The probability of winning is 3⁄100. What is the expected value of the amount that you, the player, stand togain?

a) -1.90

b) -3.00

c) -2.10

d) -2.00

e) 2.00

f) None of the above

Question 12

A random sample of 2 measurements is taken from the following population of values: -1, 0, 2, 3, 6. What isthe probability that the range of the sample is 3?

a) 0.1

b) 0.6

c) 0.3

d) 0.5

e) 0.4

f) None of the above

Question 13

A furniture store is having a sale on sofas and you're going to buy one. The advertisers know that buyers getto the store and that 1 out of 11 buyers change to a more expensive sofa than the one in the sale

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advertisement. Let X be the cost of the sofa. What is the average cost of a sofa if the advertised sofa is $100and the more expensive sofa is $375?

a) 237.50

b) 124.89

c) 350.00

d) 122.92

e) 125.00

f) None of the above

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PRINTABLE VERSIONQuiz 4

Question 1

Suppose you have a distribution, X, with mean = 9 and standard deviation = 5. Define a new randomvariable Y = 8X - 4. Find the mean and standard deviation of Y.

a) E[Y] = 68; σY = 40

b) E[Y] = 72; σY = 320

c) E[Y] = 72; σY = 36

d) E[Y] = 68; σY = 36

e) E[Y] = 68; σY = 320

f) None of the above

Question 2

Which statement is not true for a binomial distribution with n = 10 and p = 1/20 ?

a) The highest probability occurs when x equals 0.5000

b) The probability that x equals 1 is 0.3151

c) The number of trials is equal to 10

d) The mean equals 0.5000

e) The standard deviation is 0.6892

f) None of the above

Question 3

In testing a new drug, researchers found that 3% of all patients using it will have a mild side effect. Arandom sample of 5 patients using the drug is selected. Find the probability that none will have this mild sideeffect.

a) 0.8587

b) 0.0300

c) 0.1413

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d) 0.9700

e) 0.5589

f) None of the above

Question 4

In testing a new drug, researchers found that 6% of all patients using it will have a mild side effect. Arandom sample of 12 patients using the drug is selected. Find the probability that at least one will have thismild side effect.

a) 0.9400

b) 0.0600

c) 0.3292

d) 0.5241

e) 0.6605

f) None of the above

Question 5

In testing a new drug, researchers found that 2% of all patients using it will have a mild side effect. Arandom sample of 15 patients using the drug is selected. Find the probability that exactly two will have thismild side effect.

a) 0.03230

b) 0.04230

c) 0.08230

d) 0.05230

e) 0.07230

f) None of the above

Question 6

A manufacturer of matches randomly and independently puts 15 matches in each box of matches produced.The company knows that one-tenth of 9 percent of the matches are flawed. What is the probability that amatchbox will have one or fewer matches with a flaw?

a) 0.007930

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b) 0.9921

c) 0.9910

d) 0.1190

e) 0.8732

f) None of the above

Question 7

Suppose you have a binomial distribution with n = 15 and p = 0.8. Find P(9 ≤ X ≤ 11).

a) 0.3777

b) 0.2461

c) 0.3337

d) 0.1461

e) 0.5337

f) None of the above

Question 8

Each year a company selects a number of employees for a management training program. On average, 30percent of those sent complete the program. Out of the 21 people sent, what is the probability that exactly 4complete the program?

a) 0.1983

b) 0.1127

c) 0.2983

d) 0.3127

e) 0.1567

f) None of the above

Question 9

Each year a company selects a number of employees for a management training program. On average, 40percent of those sent complete the program. Out of the 41 people sent, what is the probability that 12 or morecomplete the program?

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a) 0.8945

b) 0.1054

c) 0.2054

d) 0.0566

e) 0.9433

f) None of the above

Question 10

A fish tank in a pet store has 21 fish in it. 10 are orange and 11 are white. Determine the probability that ifwe select 4 fish from the tank, at least 2 will be white.

a) 0.7443

b) 0.9643

c) 0.2556

d) 0.2776

e) 0.5238

f) None of the above

Question 11

Identify the following distribution as binomial, geometric or neither. There is a probability of 0.08 that a vaccine will cause a certain side effect. Suppose that a number of

patients are inoculated with the vaccine. We are interested in the number of patients vaccinated until the firstside effect is observed.

a) Geometric

b) Binomial

c) Neither

Question 12

A quarter back completes 20% of his passes. We want to observe this quarterback during one game to seehow many pass attempts he makes before completing one pass. What is the probability that the quarterbackthrows 4 incomplete passes before he has a completion?

a) 0.0875

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b) 0.0819

c) 0.9180

d) 0.9344

e) 0.0655

f) None of the above

Question 13

A quarter back completes 30% of his passes. We want to observe this quarterback during one game to seehow many pass attempts he makes before completing one pass. Determine the probability that it takes morethan 12 attempts before he completes a pass.

a) 0.0138

b) 0.0041

c) 0.9861

d) 0.9958

e) 0.0261

f) None of the above

Question 14

Joe has an 28% probability of passing his statistics quiz 4 each time he takes it. What is the probability hewill take no more than 6 tries to pass it?

a) 0.0390

b) 0.1393

c) 0.0610

d) 0.9609

e) 0.8606

f) None of the above

Question 15

Joe has an 10% probability of passing his statistics quiz 4 each time he takes it. How many times should Joeexpect to take his quiz before passing it?

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a) 21

b) 12

c) 9

d) 10

e) 70

f) None of the above