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 25 mph speed​ limit, a place that in the past has been known for producing fines. The mean of 100 representative readings was 28.77 ​mph, with a standard deviation of 3.54 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 38 mph or one going 15 ​mph?

Answer 1

μ = mean = 28.77

σ = standard deviation = 3,54

We find the z score for 25 mph to for how many standard deviations from the mean would a car going the speed limit​ be

z = -1.064971751

Negative sign to Z score means below the mean

Answer :-

A car going the speed limit​ be 1.064971751 standard deviation below the mean Speed

# b part

First we find the z score for 38

z = 2.607344633

Now we find Z score 15

z = -3.889830508

Here The going speed 15 mph is more unusual with a z score of -3.889830508 below the mean than the 38 mph with 2.607344633 above the mean

( beacuse Z score - 3.889830508 too far from the standard normal distribution mean ( 0 ) )

I hope this will help you :)