The police department of a major city needs to update its budget. For this purpo
ID: 3066085 • Letter: T
Question
The police department of a major city needs to update its budget. For this purpose, they need to understand the variation in their fines collected from motorists for speeding. As a sample, they recorded the speeds of cars driving past a location with a 25 mph speed limit, a place that in the past has been known for producing fines. The mean of 100 representative readings was 28.69 mph, with a standard deviation of 3.62 mph.
a) How many standard deviations from the mean would a car going the speed limit be?
b) Which would be more unusual, a car traveling 39 mph or one going 16 mph?
a) A car traveling at the speed limit is 1.02 standard deviations from the mean. (Round to two decimal places as needed.)
b) Choose the correct answer below and fill in the answer -_________(es) to complete your choice.
A. The car traveling 16 mph is more unusual. It is______ standard deviations from the mean, while the car traveling 39 mph is ______ standard deviations from the mean. (Round to two decimal places as needed.)
B. The car traveling 39 mph is more unusual. It is _______ standard deviations from the mean, while the car traveling 16 mph is _____standard deviations from the mean. (Round to two decimal places as needed.)
C. Both cars are equally unusual. Both cars are _______standard deviations from the mean.
Explanation / Answer
Solution:- mean = 28.69 , standard deviation = 3.62 , X = 25
Formula = Z = (X - ) /
a) X = 25
=> Z = (25 - 28.69)/3.62
= -1.0193
b) X = 39
=> Z = (39 - 28.69)/3.62 = 2.8481
X = 16
=> Z = (16-28.69)/3.62 = -3.5055
=> option A. The car traveling 16 mph is more unusual. It is 3.62 standard deviations from the mean, while the car traveling 39 mph is 3.62 standard deviations from the mean. (Round to two decimal places as needed.)
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