Question

A film distribution manager calculates that 9% of the films released are flops. If the manager is accurate, what is the probability that the proportion of flops in a sample of 425 released films would differ from the population proportion by greater than 3%? Round your answer to four decimal places.

Answer 1

Solution

Given that,

p = 0.09

1 - p = 1 - 0.09 = 0.91

n = 425

= p = 0.09

=  p ( 1 - p ) / n

=   (0.09 * 0.91) / 425 = 0.01388

= 0.01388

1 - P(0.06 < < 0.12)

= 1 - P( (0.06 - 0.09) / 0.01388 < ( - ) / < (0.12 - 0.09) / 0.01388)

= 1 - P(-2.16 < z < 2.16)

= 1 - [P(z < 2.16) - P(z < -2.16)]

= 1 - [0.9846 - 0.0154]

= 1 - 0.9692

= 0.0308

Probability = 0.0308