The Weights of Five Players on a Football Team Are

Essay

The weights of five players on a football team are shown below.
$\begin{array}{r|ccccc} \text { Player } & \text { A } & \text { B } & \text { C } & \text { D } & \text { E } \\ \hline \text { Weight (lb) } & 290 & 310 & 250 & 255 & 220 \end{array}$
Consider these players to be a population of interest. The mean weight, $\mu$ , for the population is 265 pounds. Construct a table that shows all of the possible samples of size three. For each of the possible samples, list the players in the sample, their weights, and the sample mean. The first line of the table is shown below.
$\begin{array}{c|c|c} \text { Sample } & \text { Weights } & \bar{x} \\ \hline \text { A, B, C } & 290,310,250 & 283.3 \end{array}$
Use your table to find the probability that, for a random sample of size three, the sample mean will be within 15 lb of the population mean.