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​ limit, a place that in the past has been known for producing fines. The mean of 100 representative readings was 38.87 ​mph, with a standard deviation of 3.58 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 46 mph or one going 24 ​mph?

Answer 1

Answer:

Given that:

As a​ sample, they recorded the speeds of cars driving past a location with a 35 mph speed​ limit, a place that in the past has been known for producing fines. The mean of 100 representative readings was 38.87​mph, with a standard deviation of 3.58 mph.

a) How many standard deviations from the mean would a car going the speed limit​ be?

Using central limit theorem,

The going the speed limit be 10.81 standard deviation above the mean.

b) Which would be more​ unusual, a car traveling 46 mph or one going 24 ​mph?

When,

When

46 mph is more unusual.