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chapter5 homework - ECON 2300 Homework Assignment#5 1(from...

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ECON 2300 Homework Assignment #5 1. (from Chapter 6) Sales directors for a large company submit monthly expense reports to be reimbursed for expenses related to business meals. The average amount requested per month for all sales directors in the company is normally distributed with a mean of μ =$700 with a standard deviation of σ =$150. a. What percentage of sales directors for the company request more than $1000 per month for business meals? P(x>150) = P(z>(1000-700)/150 = P(z >2) 1- 0.97725 P(x>150) = .0228 or 2.28 percent b. What percentage of sales directors request $500 and $1000 a month in reimbursements? P(500< x < 1000) = P((500-700)/150 < z < (1000 - 700)/150) = P(-1.3 < z < 2) = The area under the curve associated with z = 2 is .9772; the area under the curve associated with z = -1.3 is .9032. P(500 < x < 1000) = .9772-.9032= .074 or 7.4%
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c. What is the probability that a randomly selected sales director will request less than $500 next month? P(x < 500) = P((z < (500- 700)/150)= P(z < -1.3)= P(x < 500) = .0968 or 9.68% d. What is the amount that at least 90% of sales directors request each month? 892.23
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