The shoe sizes of 36 women are measured, and their average is 8.2

a. Suppose it is known that the standard deviation of shoe size is 1.17. Find a 95% confidence interval for the average shoe size of an adult woman.

b. How large a sample of shoe sizes should we take to ensure that the margin of error of a 80% confidence interval is 0.25 shoe sizes?

c. Suppose the standard deviation of shoe size is unknown, but the standard deviation of the sample was 0.95. Find a 90% confidence interval for the average shoe size.