The lengths of adult males' hands are normally distributed with mean 188 mm and standard deviation is 7.1 mm. Suppose that 50 individuals are randomly chosen. Round all answers to 4 where possible.

1. What is the distribution of x? x^- ~ N=
2. For the group of 50, find the probability that the average hand length is more than 186=
3. Find the first quartile for the average adult male hand length for this sample size=
4. For part b), is the assumption that the distribution is normal necessary? Yes No