A Random Sample of Size 225 Is Taken from the Population

Essay

A random sample of size 225 is taken from the population of the ages of seniors enrolled at a large university one semester. This population has mean 22.3 years and standard deviation 2.5. The population distribution is not normal.
(a) Is it reasonable to assume a normal distribution for the sample mean $\bar{x}$ Why or why not?
(b) Find the probability that $\bar{x}$ lies between 22.1 and 22.5 years.

(c) Find the probability that $\bar{x}$ exceeds 22.7 years.