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## Probability values based on normal distribution.

1.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 \$40,000, and for the female graduates it is \$22,000.
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 (to 4 decimals)?
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)?
c. In which of the 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?
a.because the population mean for males is higher
b.because the population standard deviation for males is higher
c.because the population mean for females is lower
d.because the population standard deviation for females is lower
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)?

2.Sales personnel for Skilling’s Distributors submit weekly reports listing the customer contacts made during the week. A sample of 65 weekly reports showed a sample mean of 19.5 customer contacts per week. The sample standard deviation was 5.2. Provide 90% and 95% confidence intervals for the population mean number of weekly customer contacts for the sales personnel.
a)90% Confidence, to 2 decimals:
b)95% Confidence, to 2 decimals:

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