Question

The director of the library calculates that 14% of the library's collection is checked out. If the director is right, what is the probability that the proportion of books checked out in a sample of 538 books would be less than 10%? Round your answer to four decimal places.

Answer 1

Solution

Given that,

p = 14% = 0.14

1 - p = 1 - 0.14 = 0.86

n = 538

= p = 0.14

=  p ( 1 - p ) / n

=   (0.14 * 0.86) / 538 = 0.015

P( < 0.10)

= P(( - ) / < (0.10 - 0.14) / 0.015)

= P(z < -2.67)

= 0.0038

Probability = 0.0038