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Business Week conducted a survey of graduates from 30 top MBA programs. On the babsis of the survey, assume that the mean annual salary for male and female graduates 10 years after graduation is $168,000 and $117,000, respectively. Assume the standard deviation for the male graduates is $40,000 and for the females is $25,000.
a) 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?
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?
c) In which preceding two cases part a or part b do we have a higher probability of obtaining a sample estimate within $10,000 of the population mean and why?
d) What is the probability that a simple random sample of 100 male graduates will provide a sample mean more than $4000 below the population mean?
Thank you in advance for any advice or help with this question.
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