Question

mr. lee is a librarian at eastside library. in examining a random sample of the librarys book collection, he found the following.
751 books had no damage,
72 books had minor damage, and
29 books had major damage.
based on this sample, how many of the 30,000 books in the collection should mr. lee expect to have minor damage or major damage? round your answer to the nearest whole number. do not round any intermediate calculations.
books

Explanation:

Step1: Find total sample size

First, calculate the total number of books in the sample. Add the number of books with no damage, minor damage, and major damage. So, \(751 + 72 + 29 = 852\).

Step2: Find proportion of damaged books

Next, find the number of damaged books (minor + major) in the sample: \(72 + 29 = 101\). The proportion of damaged books in the sample is \(\frac{101}{852}\).

Step3: Estimate damaged books in collection

Now, multiply this proportion by the total number of books in the collection (30,000) to find the expected number of damaged books. So, \(30000\times\frac{101}{852}\). Calculate this: \(30000\times101 = 3030000\), then divide by 852: \(\frac{3030000}{852}\approx3556.338\). Rounding to the nearest whole number gives 3556.

Answer:

3556