A police radar gun is used to measure speeds of cars on a hi

A police radar gun is used to measure speeds of cars on a highway. The speeds of cars are normally distributed with the mean of 55 mi/hr and standard deviation of 5. What proportion of cars is driving between 60 and 70 mi/hr? Please show how to get the answer.

Solution

HERE MEAN = 55

STD DEV = 5

For x = 60 , z = (60 - 55) / 5 = 1 and for x = 70 , z = (70 - 55) / 5 = 3

Hence P(60 < x < 70) = P(1 < z < 3) = [area to the left of z = 3] - [area to the left of 1]

= 0.9987 - 0.8413 = 0.1574

PROPORTION = 0.1574*100 = 15.74