The lengths of adult males' hands are normally distributed with mean 191 mm and the standard deviation is 7.4 mm. Suppose that 49 individuals are randomly chosen. Round all answers to 4 where possible.
a. What is the distribution of ¯xx¯? ¯xx¯ ~ N( , )
b. For the group of 49, find the probability that the average hand length is more than 189.
c. Find the first quartile for the average adult male hand length for this sample size.
d. For part b), is the assumption that the distribution is normal necessary?