Confidence Interval and Sample Size for Carry on Luggage

See attached file for 5 questions:

Mean weight of carry-on luggage
Mean of a population
Lifetimes of washing machines
Proportion of Democrats in sample of registered voters
Proportion of customers who use stor credit card for purchases

In order to determine the average weight of carry-on luggage by passengers in airplanes, a sample of 36 pieces of carry-on luggage was weighed. The average weight was 20 pounds. Assume that we know the standard deviation of the population to be 8 pounds.
a. Determine a 97% confidence interval estimate for the mean weight of the carry-on luggage.
b. Determine a 95% confidence interval estimate for the mean weight of the carry-on luggage.
You are given the following information obtained from a random sample of 4 observations taken from a large, normally distributed population.
25 47 32 56
Construct a 95% confidence interval for the mean of the population.

If the standard deviation for the lifetimes of washing machines is estimated to be 800 hours, how large a sample must be taken in order to be 97% confident that the margin of error will not exceed 50 hours?

In a random sample of 200 registered voters, 120 indicated they are Democrats. Develop a 95% confidence interval for the proportion of registered voters in the population who are Democrats.

The manager of a department store wants to determine what proportion of people who enter the store use the store’s credit card for their purchases. What size sample should he take so that at 99% confidence the error will not be more than 8%?

Show work please.

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