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

answer; ///(d); determining who competes most closely   with whom evaluating whether industry driving forces and competitive pressure favor some strategic groups and hurt others, and ascertaining whether the profit potential of different strategic groups varies due to the strengths and weaknesses in each groups respective market positions;