Question

SA police department used a radar gun to measure the speed of a sample of cars on the highway.

Assume that the distribution of speeds is approximately Normal with a mean of 71 mph and a
standard deviation of 8 mph.
Using this distribution what is the z-score of a 65-mph speed limit? *​

Answer 1

The z score of the 65-mph speed limit is -0.75

Explanation:

The z score is given by the relation;

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

Where:

Z = Normal (Standard) or z score

x = Observed speed score

μ = Mean, expected speed

σ = Standard deviation

Where we plug in the values for x = 65-mph, σ = 8 mph and μ = 71 mph, into the z-score equation, we get;

`z = (65-71)/(8)= (-6)/(8) = -(3)/(4)`

Hence the z score of the 65-mph speed limit =-3/4 or -0.75.