a) a random sample of 15 registered nurses in a large hospital showed they worked on average 44.2 hours per week. The standard deviation of the sample was 2.6. Estimate the mean of the population with 90% confidence. ( provide an answer with two decimal places)

b) in a preliminary study, a simple random sample of 100 computer chips was a tester, and 17 of them were found to be defective. Now another sample will be drawn in order to construct a 95% confidence interval for the proportion of chips that are defective. Use the results of the preliminary study to estimate the sample size needed so that the confidence interval will have a margin of error of 0.06 ( provide answer in whole number)