Problem 18SE

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

b. Let µnail denote the mean weight of a nail. Express µnail in terms of µbox.

c. Find a 95% confidence interval for µnail.

Solution

Step 1 of 4

Given the box contains 100 nails each

The sample size is 10 boxes

The mean weight of the box

The Standard deviation of the box is