Answer:
The probability that the proportion of books checked out in a sample of 774 books would be less than 10% is 0.0066
Explanation:
We are given that The director of the library believes that 13% of the library's collection is checked out.

Total no. of books = 774
Standard deviation =

Standard deviation =

We are supposed to find the probability that the proportion of books checked out in a sample of 774 books would be less than 10%

So,

Hence the probability that the proportion of books checked out in a sample of 774 books would be less than 10% is 0.0066