Normal Probability & Confidence Interval

Please see the files attached.

Show all work.
Please do first 4 problems.

1. Business Week surveyed MBA alumni 10 years after graduation (Business Week, September 22, 2003). One finding was that alumni spend an average of $115.50 per week eating out socially. You have been asked to conduct a follow-up study by taking a sample of 40 of these MBA alumni. Assume the population standard deviation is $35.

a. Show the sampling distribution of , the sample mean weekly expenditure for the 40 MBA alumni.
b. What is the probability the sample mean will be within $10 of the population mean?
c. Suppose you find a sample mean of $100. What is the probability of finding a sample mean of $100 or less? Would you consider this sample to be an unusually low spending group of alumni? Why or why not?

20. Is your favourite TV program often interrupted by advertising? CNBC presented statistics on the average number of programming minutes in a half hour sitcom (CNBC, February 23, 2006). The following data (in minutes) are representative of their findings.
21.06 22.24 20.62
21.66 21.23 23.86
23.82 20.3 21.52
21.52 21.91 23.14
20.02 22.2 21.2
22.37 22.19 22.34
23.36 23.44

Assume the population is approximately normal. Provide a point estimate and a 95% confidence interval for the mean number of programming minutes during a half-hour television sitcom.

50. Mileage tests are conducted for a particular model of automobile. If a 98% confidence interval with a margin of error of one mile per gallon is desired, how many automobiles should be used in the test? Assume that preliminary mileage tests indicate the standard deviation is 2.6 miles per gallon.

43. Eagle Outfitters is a chain of stores specializing in outdoor apparel and camping gear. They are considering a promotion that involves mailing discount coupons to all their credit card customers. This promotion will be considered a success if more than 10% of those receiving the coupons use them. Before going national with the promotion, coupons were sent to a sample of 100 credit card customers.
a. Develop hypotheses that can be used to test whether the population proportion of those who will use the coupons is sufficient to go national
b. The file eagle contains the sample data. Develop a point estimate of the population proportion.
c. Use α = 0.05 to conduct your hypothesis test. Should Eagle go national with the promotion?