The police department of a major city needs to update its budget. For this purpo

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 30 mph speed limit, a place that in the past has been known for producing fines. The mean of 100 representative readings was 33.65 mph, with a standard deviation of 3.38 mph. a) How many standard deviations from the mean would a car gong the speed limit be? b) Which would be more unusual, a car traveling 41 mph or one going 21 mph? a) A car traveling at the speed limit is standard deviations from the mean. (Round to two decimal places as needed.)

Explanation / Answer

Answer to part a)

n = 100

M = 33.65

s = 3.36

x = 30

.

Formula of Z is as follows:

Z = (x - M) / (s)

.

On plugging the values in the formula we get:

Z = (30 - 33.65) / (3.36)

Z = 1.09

.

Thus 30 is 1.09 standard deviations away from the mean

.

Answer to part b)

The value of x that has the lagrest value of Z magnitude wise ( ro the oen that si far away from the mean is considered to be unusual)

x=41

Z = ( 41 -33.65) / 3.65

Z = 2.1875

.

x = 21

Z = (21 -33.65) / 3.36

Z = -3.76

.

Thus the value of x = 21, is farther from mean , as compared to x = 41, because |z| for x=21 is 3.76 > 2.1875

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