In: Math
Suppose men's heights are normally distributed with mean of 176 cm and variance of 25cm^2.
A. What proportion of mean are between 172 cm and 178 cm tall?
B. Find the minimum ceiling of an airplane such that at most 2% of the men walking down the aisle will have to duck their heads.
C. Suppose you take a random sample of 6 men. What is the sampling distribution of the sample mean height? Why?
D. Find the probability that the average height of a random sample of 64 men is greater than 178cm. If these heights were not normally distributed, would you still be able to answer the question? why or why not?