7. Sampling Distributions & Confidence Intervals: Mean

A puzzle company is interested in the average number of pieces in their jigsaw puzzles, so they plan to create a confidence interval for the true mean. The easiest puzzle in their line is $100$ pieces, and the largest is $1000$ pieces. Use the range rule of thumb to estimate the sample standard deviation.

A bookstore is interested in the average length of books in its adult fiction section. Find the minimum sample size required to create a $99\%$ confidence interval with a margin of error no more than $30$ pages if...

(A) The standard deviation is known to be about $96$ pages.

A bookstore is interested in the average length of books in its adult fiction section. Find the minimum sample size required to create a $99\%$ confidence interval with a margin of error no more than $30$ pages if...

(B) The standard deviation is unknown, but the longest book is $697$ pages and the shortest is $298$ pages.