The annual commissions earned by sales representatives of Machine Products Inc.,

ID: 3241550 • Letter: T

Question

The annual commissions earned by sales representatives of Machine Products Inc., a

manufacturer of light machinery, follow the normal probability 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 earn less than 28,000 per year?

c. 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?

a) P(X > 42000)

= P(z > (42000 - 40000)/5000)

= P(z > 0.40)

= 0.3446

So,

34.46% of sales representatives earn more than $42,000 per year.

b) P(X < 28000)

= P(z < (28000 - 40000)/5000)

= P(z < -2.4)

= 0.0082

Hence,

0.82% of the sales representatives earn less than $28,000.

c) From z table,

P(z > 0.84) = 0.20

Hence,

Cutoff point between those who earn a bonus and those who do not

= 40000 + 0.84(5000)

= $44,200

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