Solve the Problem Consider These Board Members to Be a Population of Interest

Essay

Solve the problem.
-The ages of six members of a board of directors of a nonprofit organization are shown below.
$\begin{array}{r|cccccc} \text { Member } & \text { A } & \text { B } & \text { C } & \text { D } & \text { E } & \text { F } \\ \hline \text { Age } & 32 & 52 & 43 & 64 & 41 & 50 \end{array}$
Consider these board members to be a population of interest. The mean age, $\mu$ , for the population is 47. Construct a table that shows all of the possible samples of size five. For each of the possible samples, list the people in the sample, their ages, and the sample mean. The first line of the table is shown below. $\begin{array}{c|c|c} \text { Sample } & \text { Ages } & \bar{x} \\ \hline \text { A }, B, C, D, E & 32,52,43,64,41 & 46.4 \end{array}$
Use your table to find the probability that, for a random sample of size five, the sample mean will be within 2 years of the population mean.