Use the normal distribution or the t-distribution to construct a 90% and 99% confidence interval for the population mean. Justify your answer. If neither distribution can be used, explain why. Interpret the results and compare the widths of the confidence intervals.

1. In a random sample of 15 mortgage institutions, the mean interest rate was 4.99% and the standard deviation was 6.12. Assume the interest rates are normally distributed.
2. In a recent season, the standard deviation of the yards per carry of all running backs was 1.34. The yards per carry of 20 randomly selected running backs are listed below. Assume the yards per carry are normally distributed.

5.6, 4.4, 3.8, 4.5, 3.3, 5.0, 3.6, 3.7, 4.8, 3.5, 5.6, 3.0, 6.8, 4.7, 2.2, 3.3, 5.7, 3.0, 5.0, 4.5

3.In a random sample of 13 people, the mean length of stay at a hospital was 6.3 days and the standard deviation was 1.7 days. Assume the lengths

of stay are normally distributed.