Question

A film distribution manager calculates that 9% of the films released are flops. If the manager is correct, what is the probability that the proportion of flops in a sample of 701 released films would be greater than 7%? Round your answer to four decimal places. Please show how to enter short hand in calculator.

Answer 1

The probability that the proportion of flops in a sample of 701 released films would differ from the population proportion by greater than 7% is 0.00001

Explanation:

We are given;

Probability that the films released are flops = 9% = 0.09

Sample size = 701

Formula for standard deviation is;

σ = √(p(1 - p)/n)

σ = √(0.09(1 - 0.09)/701)

σ = √0.0001168331

σ = 0.0108

We want to find the probability that the proportion of flops in a sample of 701 released films would be greater than 7%.

Thus, it means x - μ = 7% = 0.07

Z-score formula here is;

z = (x - μ)/σ

z = 0.07/0.0108

z = 6.4815

From online p-value from z-score calculator attached using; z = 6.4815, Nominal significance level = 0.05, two tailed distribution, we have;

P-value = 0.00001