Question 912323: 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? (Round z-score computation to 2 decimal places and your final answer to 2 decimal places.)
(b) What percent of the sales representatives earn between $32,000 and $42,000? (Round z-score computation to 2 decimal places and your final answer to 2 decimal places.)
(c) What percent of the sales representatives earn between $32,000 and $35,000? (Round z-score computation to 2 decimal places and your final answer to 2 decimal places.)
(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? (Round your answer to the nearest dollar amount.)
Answer by ewatrrr(24785)   (Show Source):
You can put this solution on YOUR website! m = 40,000, sd = 5000
a) 1 - P(x ≤ 42,000) = 1 - p(z ≤ (42000-40000)/5000)) = 1 - P( z ≤ .4) = 1 - .6554 = 1- .66 = .34 0r 34%
b) P = normalcdf(32,000,42,000,40,000,5000) Using TI
or P(z < .4) - P(z < - 1.6) = .6554 - .0548 = .66 - .05 = .61 0r 61%
c) P = normalcdf(32,000,35,000,40,000,5000)
d) 5000invNorm(.80) + $40,000 = X,
5000(.84) + $40,000 = X
the cutoff point between those who earn a bonus and those who do not
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