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?

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

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