A 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?

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

Step-by-step explanation:

Here, we want to calculate the z-score

To calculate the z-score, we make use of the z-score formula

Mathematically;

z-score = (x-mean) / SD

from the question we identify the values as x = 65 mph, mean = 71 mph, Standard deviation (SD) = 8 mph

Plugging these values into the equation above, we have

z-score = (65-71) / 8 = - 6/8 = - 0.75