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 435 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- = 0.91

n = 435

= p = 0.09

= (p*(1-p))/n =  (0.09*0.91)/435 = 0.01372

P(0.05 < <0.13 ) = P((0.05-0.09)/0.01372 ) < ( - ) /  < (0.13-0.09) /0.01372 ) )

= P(-2.915 < z < 2.915 )

= 1-(P(z < 2.915) - P(z < -2.915))

= 1 - ( 0.9982 - 0.0018)

= 1 - 0.9964

= 0.0036

Probability = 0.0036

The probability that the proportion of flops in a sample of 435 released films would differ from the population proportion by greater than 4% is 0.0036