Question

mr. powell is a librarian at central library. in examining a random sample of the library’s book collection, he found the following. 943 books had no damage, 53 books had minor damage, and 29 books had major damage. based on this sample, how many of the 58,000 books in the collection should mr. powell expect to have no damage? round your answer to the nearest whole number. do not round any intermediate calculations.

Explanation:

Step1: Calculate total sample size

First, find the total number of books in the sample. Add the number of books with no damage, minor damage, and major damage. So, \(943 + 53 + 29 = 1025\).

Step2: Find the proportion of undamaged books

The proportion of books with no damage in the sample is \(\frac{943}{1025}\).

Step3: Estimate undamaged books in collection

Multiply this proportion by the total number of books in the collection (58,000) to find the expected number of undamaged books. So, \(58000\times\frac{943}{1025}\). Calculate this: \(58000\div1025 = 56.58536585\), then multiply by 943: \(56.58536585\times943 \approx 53360\) (after rounding to the nearest whole number).

Answer:

53360