Business Week conducted a survey of graduates from 30 top MBA programs (Business Week, September 22, 2003). The survey found...

Business Week conducted a survey of graduates from 30 top MBA programs (Business Week, September 22, 2003). The survey found that the average annual salary for male and female graduates 10 years after graduation was $168,000 and $117,000, respectively. Assume the population standard deviation for the male graduates is $45,000, and for the female graduates it is $22,000
1. What is the probability that a simple random sample of 40 male graduates will provide a sample mean within $10,000 of the population mean, $168,000 (to 4 decimals)?
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t(158000) = (158000-168000)/[45000/sqrt(40)] = -1.3055
t(178000) = +1.3055
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P(-1.3055<= t <=1.3055 with df = 39) = 0.8006
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2. b.What is the probability that a simple random sample of 40 female graduates will provide a sample mean within $10,000 of the population mean, $117,000 (to 4 decimals)?
Note: Same procedure as done above for the males.
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3. d.What is the probability that a simple random sample of 100 male graduates will provide a sample mean more than $4,000 below the population mean (to 4 decimals)?
t(164000) = (164000-168000/[45000/sqrt(100)) = -0.8889
P(xbar < 164000) = tcdf(-100,-0.8889,99) = 0.1881