In order to control costs, a company desires to study the amount of money its sales force spends entertaining clients. The following is random sample of six entertainment expenses (dinner costs for four people) from expense reports submitted through members of the sales force.
$157 $132 $109 $ 145 $125 $139
a. Compute x [its x with a bar over it which is the sample mean], s squared (sample variance), and s (sample standard deviation) for the expense data. In addition show that the two different formulas for calculating s squared give the same result.
b. Supposing that the distribution of entertainment expenses is approximately normally distributed, calculate estimates of tolerance intervals containing 68.26 percent, 95.44 percent, and 99.73 percent of all entertainment expenses by the sales force.
c. If a member of sales force submits an entertainment expense (dinner cost for four) of $190, should this expense be considered unusually high (and possibly worthy of investigation by the company? Explain your answer.
d. Calculate and interpret the z-score for each of the six entertainment expenses.