Question

A hotel manager believes that 14% 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 804 rooms would be less than 13%?

Answer 1

0.4996

Explanation:

We are given;

Population proportion; p = 14% = 0.14

Sample size; n = 804

Sample proportion; p^ = 13% = 0.13

Standard deviation; σ = √np(1 - p)

σ = √(804 × 0.14 × (1 - 0.14))

σ = 9.8388

Formula for z-score is;

z = (p^ - p)/σ

z = (0.13 - 0.14)/9.8388

z = -0.01/9.8388

z = -0.001

From online z-score and probability converter attached, we have;

P(Z < -0.001) = 0.4996