Business, 15.02.2020 01:53 Fireburntbudder

The annual commissions earned by sales representatives of Machine Products Inc., 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 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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Answer from: bryantjorell

a. What percent of the sales representatives earn more than $42,000 per year?

z = (42000-40000)/5000 z = 0.4 prob(z > 0.4) = 0.3446

b. What percent of the sales representatives earn between $32,000 and $42,000?

z(32000) = (32000-40000)/5000 = -1.6 prob(-1.6 < z < 0.4) = 0.6006

c. What percent of the sales representatives earn between $32,000 and $35,000?

z(35000) = (35000-40000)/5000 = -1 prob(-1.6 < z < -1) = 0.1039

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?

z(20%) = 0.8416 x = z*sigma + mu x = 0.8416*5000 + 40000 x = $44208

Answer from: Quest

It’s option c for sure

Answer from: Quest

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