Mrs. Moore is a librarian at Westside Library. In examining a random sample of the library's book collection, she found the following.
794 books had no damage,
71 books had minor damage, and
30 books had major damage.
Based on this sample, how many of the 57,000 books in the collection should Mrs. Moore expect to have minor damage or major damage? Round your answer to the nearest whole number. Do not round any intermediate calculations.
books
Based on the proportions in the sample, we can calculate the expected number of books with minor or major damage in the entire collection.
First, calculate the proportion of books with minor damage in the sample:
Proportion of minor damage = (71 books with minor damage) / (794 total books) = 71/794 ≈ 0.08942
Next, calculate the proportion of books with major damage in the sample:
Proportion of major damage = (30 books with major damage) / (794 total books) = 30/794 ≈ 0.03778
Now, calculate the expected number of books with minor or major damage in the entire collection:
Expected number of books with minor damage = 0.08942 * 57,000 = 5,099.94 ≈ 5,100 books
Expected number of books with major damage = 0.03778 * 57,000 = 2,156.26 ≈ 2,156 books
Therefore, Mrs. Moore should expect to have approximately 5,100 books with minor damage and 2,156 books with major damage in the entire collection.
wrong answer
Apologies for the mistake. Let's recalculate the expected number of books with minor or major damage in the entire collection.
Proportion of books with minor damage in the sample = 71 / (794 + 71 + 30) = 71 / 895 ≈ 0.07933
Proportion of books with major damage in the sample = 30 / 895 ≈ 0.03352
Expected number of books with minor damage = 0.07933 * 57,000 ≈ 4,525 books
Expected number of books with major damage = 0.03352 * 57,000 ≈ 1,910 books
Therefore, Mrs. Moore should expect to have approximately 4,525 books with minor damage and 1,910 books with major damage in the entire collection.