# Descriptive Statistics and Normal Distribution

In order to control costs, a company wishes to study the amount of money its sales force spends entertaining clients. The following is a random sample of six entertainment expenses (dinner costs for four people) from expense reports submitted by members of the sales force. $157, $132, $109, $145, $125, $139

a) Calculate xbar, s^2, and s for the expenses data. In addition, show that the two different formulas for calculating s^2 give the same result.

b) Assuming 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 the 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) Compute and interpret the Z score for each of the six entertainment expenses

#### Solution Preview

In order to control costs, a company wishes to study the amount of money its sales force spends entertaining clients. The following is a random sample of six entertainment expenses (dinner costs for four people) from expense reports submitted by members of the sales force. $157, $132, $109, $145, $125, $139

a) Calculate x/-, s/2, and s for the expenses data. In addition, show that the two different formulas for calculating s/2 give the same result.

b) Assuming that the distribution of entertainment expenses is approximately normally ...

#### Solution Summary

The solution illustrates the application of normal distribution for summarizing numerical data. Step-by-step calculations are provided for a number of statistic calculations. The solution is provided in Word doc and pdf form.