Discuss the below:
Q: Hal recently accepted a sales position with (IBM) selling "big iron" (mainframe computers). He has to decide between taking a salary only or taking a smaller salary plus commissions on sales. As part of his decision-making process, he has collected historical data from previous years on the number of mainframe sales made by individual salespeople at IBM. Following is the probability distribution for X = number of mainframes sold in one year by a single salesperson:
X Px(x)
0 .38
1 .30
2 .15
3 .10
4 .05
5 .02
a. Compute the expected number of mainframes that Hal will sell in one year.
b. Compute the standard deviation of X.
c. Under the "salary plus commission" option, Hal will receive a base salary of $30,000 and earn $20,000 in commission from each mainframe sale. Compute Hal's expected annual salary and the standard deviation in annual salary.
d. If he takes the "salary only" option, Hal will be paid $52,000 annually. Which of the two options would you recommend that the take? Explain your answer.