Question

A film distribution manager calculates that 9% of the films released are flops. If the manager is right, what is the probability that the proportion of flops in a sample of 457 released films would differ from the population proportion by greater than 4% ? Round your answer to four decimal places.

Answer 1

Solution

Given that,

p = 0.09

1 - p = 1 - 0.09 = 0.91

n = 457

= p = 0.09

=  p ( 1 - p ) / n

=   (0.09 * 0.91) / 457 = 0.0134

= 0.0134

1 - P(0.05 < < 0.13) = 1 - P( (0.05 - 0.09) / 0.0134 < ( - ) / < (0.13 - 0.09) / 0.0134)

= 1 - P(-2.985 < z < 2.985)

= 1 - [P(z < 2.985) - P(z < -2.985)]

= 1 - [0.9986 - 0.0014]

= 1 - 0.9972

= 0.0028

Probability = 0.0028