Chapter 9, Problem 18SE

Student Ages The mean age of all 2550 students at a small college is $22.8$ years with a standard deviation is $3.2$ years, and the distribution is right-skewed. A random sample of 4 students’ ages is obtained, and the mean is $23.2$ with a standard deviation of $2.4$ years.

a. $\mu =?\sigma =?\bar{x}=?s=?$

b. Is m a parameter or a statistic?

c. Are the conditions for using the CLT fulfilled? What would be the shape of the approximate sampling distribution of many means, each from a sample of 4 students? Would the shape be right-skewed, Normal, or left-skewed?