Help Please:

Designing Motorcycle Helmets. Engineers must consider the breadths of male heads when designing motorcycle helmets. Men have head breadths that are normally distributed with a mean of 6.0 inches and a standard deviation of 1.0 inches (based on anthropometric survey data from Gordon, Churchill, et al.) (5pts)

a) If one male is randomly selected, find the probability that his head breadth is less than 6.2 inches.

First compute the z score for X= 6.2 inches and then compute the probability, P(X < 6.2 inches). Round the z score to 2 decimal places and the probability to 4 decimal places.

b) The Safeguard Helmet Company plans an initial production run of 1200 helmets. Find the probability that 100 randomly selected men have a mean head breadth less than 6.2 inches.

First compute the z score for the sample mean 6.2 inches for 100 randomly selected men, then find compute the probability, P(sample mean < 6.2 inches). Round the z score to 2 decimal places and the probability to 4 decimal places.

c) The production manager sees the result from part (b) and reasons that all helmets should be made for men with head breadths less than 6.2 inches because they would fit all but a few men. Is this a reasonable argument?