Question

A film distribution manager calculates that 6% of the films released are flops.

If the manager is correct, what is the probability that the proportion of flops in a sample of 681681 released films would be greater than 8% Round your answer to four decimal places.

Answer 1

Here, μ = 0.06, σ = 0.0091 and x = 0.08. We need to compute P(X >= 0.08). The corresponding z-value is calculated using Central Limit Theorem

z = (x - μ)/σ
z = (0.08 - 0.06)/0.0091 = 2.2

Therefore,
P(X >= 0.08) = P(z <= (0.08 - 0.06)/0.0091)
= P(z >= 2.2)
= 1 - 0.9861 = 0.0139