Question

A hotel manager believes that 17% of the hotel rooms are booked.

If the manager is right, what is the probability that the proportion of rooms booked in a sample of 465 rooms would be less than 14%? Round your answer to four decimal places.

Answer 1

Solution

Given that,

p = 0.17

1 - p = 1 - 0.17 = 0.83

n = 465

= p = 0.17

=  p ( 1 - p ) / n

=   (0.17 * 0.83) / 465 = 0.01742

P( < 0.14) =

= P(( - ) / < (0.14 - 0.17) / 0.01742)

= P(z < -1.72)

= 0.0427

Probability = 0.0427