Question

A film distribution manager calculates that 4% of the films released are flops.

If the manager is correct, what is the probability that the proportion of flops in a sample of 747 released films would be greater than 3%? Round your answer to four decimal places.

Answer 1

Answer:

Given that,

A film distribution manager calculates that 4% of the films released are flops.

If the manager is correct.

What is the probability that the proportion of flops in a sample of 747 released films would be greater than 3%:

The proportion of films released are flops:

p=4/100=0.04

The sample size: n= 747

The sample proportion follows a normal distribution with a mean and standard deviation

=0.0072 (Approximately)

The probability that the proportion of flops in a sample of 747 released films would be greater than 3%=P( > 0.03).

P( > 0.03)=1- P( 0.03)

Z-score for 0.03 is=(0.03-)/

=(0.03-0.04)/0.0072

=-0.01/0.0072

Z-score=-1.3889 (Approximately)

From standard normal tables,

P( Z -1.3889)=1- P(Z Z -1.3889)

=1-0.9177

=0.0823

P( 0.03)=P( Z -1.3889)=0.0823

P( > 0.03)=1-P( 0.03)

=1-0.0823

=0.9177

Therefore, the probability that the proportion of flops in a sample of 747 released films would be greater than 3% =0.9177.