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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?

Respuesta :

ofentsemaphalla

Answer:

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

Parrain

Based on the probability distribution, the mean yearly amount, and the standard deviation, the following are true:

  1. 34.5%
  2. 60.1%
  3. 10.4%
  4. $44,208

What percent earn more than $42,000?

z = (Amount earned - Mean amount earned) / Standard deviation

= (42,000 - 40,000) / 5,000

= 0.4

Using the z table, z > 4:

= 34.5%

What percent earn between $32,000 and $42,000?

z for 32,000 would be:

= (32,000 - 40,000) / 5,000

= -1.6

Using z table, (-1.6 < z <0.4)

= 60.1%

What percent earn between $32,000 and $35,000?

z for 35,000 would be:

= (35,000 - 40,000) / 5,000

= -1

Using z table ( -1.6 < z < -1)

= 10.4%

What would be the cutoff point?

= z value for 20% x Standard deviation + Mean earnings

= 0.8416 x 5,000 + 40,000

= $44,200 approx.

Find out more on z values at https://brainly.com/question/25638875.

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