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Mean Annual Commissions

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The annual commissions earned by sales representatives of Machine Products, Inc. a manufacturer of light machinery, follow the normal distribution. The mean yearly amount earned is $40,000 and the standard deviation is $5,000.

a. What percent of the sales representatives earn more than $42,000 per year?
b. What percent of the sales representatives earn between $32,000 and $42,000?
c. What percent of the sales representatives earn between $32,000 and $35,000?
d. The sales manager wants to award the sales representatives who earn the largest commissions a bonus of $1,000. He can award a bonus to 20 percent of the representatives. What is the cutoff point between those who earn a bonus and those who do not?

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