A 90% confidence interval for p is
So you want
You don't know in part (A), (in part (B) is 12/60) but you can use the fact that
Now all you have to do is solve for n.
The director of a museum would like to know what fraction of the museum associates make purchases through the gift shop catalog
A) If no preliminary study is done, how large a sample must be taken if the director is to say with 90% confidence that the sample estimate is within 2% of the population proportion?
B) A preliminary study showed that out of 60 associates 12 have used the gift shop catalog, what size sample does the director need in order to say with 90% confidence that the sample estimate is within 2% of the population proportion??
Any guidance would be much appreciated, not exactly sure how to start with this one, thanks in advance for any help