Gain Communications. Example 4.16 provides the probability distribution for military sales X and the mean of X. From this section, we learned that the mean of a probability distribution describes the long-run average outcome. In this exercise, you will explore this concept using technology.

• Excel users: Input the values 1000, 3000, 5000, and 10000 in the first four rows of column A. Now input the corresponding probabilities of 0.1, 0.3, 0.4, and 0.2 in the first four rows of column B. Now choose “Random Number Generation” from the Data Analysis menu box (refer to the Appendix of Chapter 1 for installing the Data Analysis ToolPak). Enter “1” in the Number of Variables box, enter “20000” in the Number of Random Numbers box, choose “Discrete” for the Distribution option, enter the cell range of the X-values and their probabilities

($A$1:$B$4) in the Value and Probability Input Range box, and finally select Row 1 of any empty column for the Output Range. Click OK to find 20,000 realizations of X outputted in the worksheet. Using Excel’s AVERAGE( ) function, find the average of the 20,000 X-values.

• Minitab users: Input the values 1000, 3000, 5000, and 10000 in the first four rows of column 1 (c1). Now input the corresponding probabilities of 0.1, 0.3, 0.4, and 0.2 in the first four rows of column 2 (c2). Do the following pull-down sequence: Calc

→Random Data→Discrete. Enter “20000” in the Number of rows of data to generate box, type “c3” in the Store in column(

s) box, click in “c1” in the Values in box, and click in “c2”

in the Probabilities in box. Click OK to find 20,000 realizations of X outputted in the worksheet. Find the average of the 20,000 X-values.

Whether you used Excel or Minitab, how does the average value of the 20,000 X-values compare with the mean reported in Example 4.16?