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 33.74 mph, with a standard deviation of 3.26 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 43 mph or one going 20 mph? a) A car traveling at the speed limit is standard deviations from the mean. Round to two decimal places as needed.)

Answer 1

a )

z = $\bar{x}$ - $\mu$ / S

z = 33.74 - 30 / 3.26

= 1.15

b)

When $\bar{x}$ = 43

z = 43 - 30 /3.26

= 3.99

When $\bar{x}$ = 20

z =  20 - 30 / 3.26

= -3.07

43 mph would be more unusual.