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 38.74 ​mph, with a standard deviation of 3.31 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 48 mph or one going 25 ​mph?

Answer 1

a) - 1.13

b) The speed of 25 mph is more unusual.

Explanation:

Given:

Speed limit = 35 mph

Mean of speeds, μ = 38.74 mph

standard deviation, σ = 3.31 mph

a) Now,

thus,

for x = 35 mph

`z=(x-\mu)/(\sigma)`

here,

z is the deviation from the mean

`z=\frac{\textup{35-38.74}}{\textup{3.31}}`

or

z = - 1.129 ≈ - 1.13

b) now,

for x = 48

`z=\frac{\textup{48-38.74}}{\textup{3.31}}`

or

z = 2.79

and, for x = 25 mph

`z=\frac{\textup{25-38.74}}{\textup{3.31}}`

or

z = -4.15

on comparing the results we can see that 25 mph is more deviated from the mean, thus the speed of 25 mph is more unusual.