A radar unit is used to measure the speed of auto-mobiles on an expressway during rush-hour traffic. The speeds of individual automobiles are normally distributed with a mean of 62 mph.
a. Find the standard deviation of all speeds if 3% of the automobiles travel faster than 72 mph.
b. Using the standard deviation found in part a, find the percentage of these cars that are traveling less than 55 mph.
c. Using the standard deviation found in part a, find the 95th percentile for the variable “speed.”