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 35 mph speed imit, a place that in the past has been known for producing fines. The mean of 100 representative readings was 38.72 mph, with a standard deviation of 3.69 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 45 mph or one going 25 mph?

Explanation / Answer

= 38.72 = 3.69

a) X = 35

Z = (X - ) /

= (35 - 38.72) / 3.69

= -1.008 standard deviations.

b) X = 45

Z = (45 - 38.72) / 3.69

= 1.7019

X = 25

Z = (25 - 38.72) / 3.69

= -3.7182

Since the value of 25 is deviated more from the mean, the car travelling at 25mph is more unusual.

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