The sitting height (from seat to top of head) of drivers must be considered in the design of a new car model. Men have sitting heights that are normally distributed with a mean of 36.0 in. and a standard deviation of 1.4 in. (based on anthropometric survey data from Gordon, Churchill, et al.).
a. One car is designed to accommodate sitting heights of 38.8 in. or less. Find the percentage of men with sitting heights greater than 38.8 in.
b. If the sitting height is to be changed so that 98% of men will be accommodated, what is the new sitting height?
c. If a car is occupied by four men, find the probability that they have a mean sitting height less than 37.0 in.