Question

Historically, the probability that a library book will be returned at the university library in one week is .40. A random sample of 10 books is taken in one week. a. What is the probability that 8 books will be returned? b. Assuming this result is observed, what conclusion could the head librarian make about the historical rate of return?

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Answer 1

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a. P(return 8 out of 10 books will be written in a week) ?

So, that can be modelled using Binomial distribution using parameters, p = .4, n = 10, x = 8

P(X,n,p)
= P(8,10,.4)
= 10C8*(.4^8)*(.6^2)
= 0.01062

Answer: 0.01062

b.

Assuming this result is observed, the conclusion that the head librarian can make about the historical rate of return is that the probability of returning 8 books out of 10 is practically nothing i.e. it is very unusual to return 8 out of 10 books within a week.