Example problems from Chapter 2: Modeling Distributions of Data

Pg. 106/#8 PERCENTILES

ANSWERS:

a)Estimate the x and y coordinates of Maryland: (12-12.5, 73) Maryland has approximately 12-12.5% of the population foreign-born which falls at about the 73rd percentile. Maryland has the same or more foreign born residents than 73% of the 50 states.

b) Use the y-axis to locate the 30th percentile then draw a horizontal line from this point to the intersection of the graph. Draw a perpendicular to the x-axis to determine the value which ends up being about 4% foreign born.

Pg. 106/#11 CALCULATING Z SCORES

Answer: Eleanor: (680-500)/100 = 1.8 Gerald: (27-18)/6 = 1.5 Eleanor scored comparatively higher than Gerald.

Pg. 107#19 EFFECT OF ADDING/SUBTRACTING/MULTIPLYING/DIVIDING ON DATA

Answers:

a) 69.188+18=87.188 mean 69.5+18=87.5 medianb) The std dev and IQR will not change – you just moved the entire graph 18 inches over

Pg. 108/#27 UNIFORM DISTRIBUTIONS

Answers:

a) All the probabilities are positive and the total of all probabilities = 1b) This would be a rectangle with height 1/3 and base 1 so (1/3)(1)=1/3 of the accidents occur in

the first milec) This rectangle has height 1/3 and base 1.1-.8=.3 so (1/3)(.3)=1/10 so 1/10 of the accidents occur

in front of Sue’s property.

Pg. 132/#53 Z SCORES AND PERCENTILES

Answers:

a) X=240 z=(240-266)/16 = -1.625 area under curve from -1000 to -1.625 = .0521 so approximately the 5th percentile

b) Find the z scores for 240 and 270: already have 240 so (270-266/16) = .25 Now find area of the curve between -1.625 and .25 Normal cdf(-1.625,.25) = .5466 so about 55%

c) Find the z score at 80% then use formula to find what length that would be: invNorm(.8)=.8416.84 = (x-266)/16 x=279.5 days