Question

Mr. Foster is a librarian at Eastside Library. In examining a random sample of the library's book collection, he found the following.

722 books had no damage,
75 books had minor damage, and
29 books had maior damage.

Based on this sample, how many of the 70,500 books in the collection should Mr. Foster expect to have no damage or minor damage? Round your answer to the nearest whole number. Do not round any intermediate calculations.

Answer 1

The number of books that had no damage or minor damage in the sample is:

722 + 75 = 797

To estimate the number of books in the entire collection that would have no damage or minor damage, we can assume that the proportion of books with no or minor damage in the sample is approximately equal to the proportion of books with no or minor damage in the entire collection.

The proportion of books with no or minor damage in the sample is:

797 / (722 + 75 + 29) = 0.9064

So we can estimate the number of books with no damage or minor damage in the entire collection as:

0.9064 x 70,500 = 63,912.6

Rounding to the nearest whole number, we get:

63,913