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 
denote the mean weight of a box of nails. Find a 95% confidence interval for .
b. Let 
denote the mean weight of a nail. Express in terms of .
c. Find a 95% confidence interval for .
(c) From part (a), we are 95% confident that the mean weight of a box of 100 nails is in the interval (1496.4, 1503.6). Therefore we are 95% confident that the mean weight of a single nail is in the interval(14.964, 15.036).
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