Normal Probability and Confidence Interval for a Fish Market

1) The owner of a fish market has an assistant who has determined that the weights of catfish are normally distributed, with mean of 3.2 pounds and standard deviation of 0.8 pound. What percentage of samples of 4 fish will have sample means between 3.0 and 4.0 pounds?

2) A survey of working women in North America was conducted by the Clinique unit of Estee Lauder Cosmetics. Of the 1,000 women surveyed, 55% believed that companies should hold positions for those on maternity leave for six months or less, and 45% felt that they should hold those positions for more than six months ("Work Week," The Wall Street Journal, September 11, 2001, A1). The 90% confidence interval for the proportion of all working women in North America who believe that companies should hold positions for those on maternity leave for more than six months is:

3) An economist is interested in studying the incomes of consumers in a particular region. The population standard deviation is known to be $1,000. A random sample of 50 individuals resulted in an average income of $15,000. What is the upper end point in a 99% confidence interval for the average income?

4) A university dean is interested in determining the proportion of students who receive some sort of financial aid. Rather than examine the records for all students, the dean randomly selects 200 students and finds that 118 of them are receiving financial aid. If the dean wanted to estimate the proportion of all students receiving financial aid to within 3% with 99% reliability, how many students would need to be sampled?

5) A major department store chain is interested in estimating the average amount its credit card customers spent on their first visit to the chain's new store in the mall. Fifteen credit card accounts were randomly sampled and analyzed with the following results: = $50.50 and s2 = 400. Assuming the distribution of the amount spent on their first visit is approximately normal, what is the shape of the sampling distribution of the sample mean that will be used to create the desired confidence interval for ?