Boxes of nails contain 100 nails each. A sample of 10 boxes is drawn, and each of the boxes is weighed. The average weight is 1500 g and the standard deviation is 5 g. Assume the weight of the box itself is negligible, so that all the weight is due to the nails in the box.

a. Let μ_box denote the mean weight of a box of nails. Find a 95% confidence interval for μ_box.

b. Let μ_nail denote the mean weight of a nail. Express μ_nail in terms of μ_box.

c. Find a 95% confidence interval for μ_nail.