1. The annual sales commissions earned by sales representatives of a manufacturer of light machinery

follow the normal probability distribution. The mean yearly amount earned is $40,000 and the standard

deviation us $5,000.

a. What percent of the sales representatives earn more than $43,000 per year?

b. What percent of the sales representatives earn between $37,000 and $43,000?

c. The sales manager wants to award a bonus of $1,000 to the top 20% sales representatives who earn the largest commissions. What is the cut-off point between those who earn a bonus and those who do not?

2. The average cost per night of a hotel room in New York City is $275. Assume this estimate is based on

a sample of 45 hotels and that the sample standard deviation is $60.

a. With 95% confidence, what is the margin of error?

b. What is the 95% confidence interval estimate of the population mean?

c. What is the 99% confidence interval estimate of the population mean?

d. Explain what happens to the margin of error and the confidence interval as the confidence level is increased?