can I have help with this question. this called finding areas under the normal c

Question

can I have help with this question. this called finding areas under the normal curve.

ucts Inc., a 40) 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? 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 $35,0002 d. The sales manager wants to award the sales representatives who earn the largest 4 0 commissions a bonus of $1,000. He can award a bonus to 20% of the represen- tatives. What is the cutoff point between those who earn a bonus and those who do not? 0 2

Explanation / Answer

Mean is 40000 and sd is 5000

a) P(x>42000)=P(z>(42000-40000)/5000)=P(z>0.4)= 1-P(z<0.4), from the normal distribution table we get 1-0.6554 = 0.3446

b) P(32000<x<42000)= P((32000-40000)/5000<z<(42000-40000)/5000)=P(-1.6<z<0.4)=P(z<0.4)-(1-P(z<1.6))=0.6554-(1-0.9452)=0.6006

c) P(32000<x<35000)= P((32000-40000)/5000<z<(35000-40000)/5000)=P(-1.6<z<-1) or P(1<z<1.6) or P(z<1.6) - P(z<1) =0.9452-0.8413 =0.1039

d) We need to find the z value for 0.2 probability, looking at the normal distribution table we see that the z value corresponding to 0.8 is 0.84. Thus the z value for 1-0.8 or 0.2 is -0.84

Thus (x-40000)/5000 = -0.84 or x is 35800

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