A film distribution manager calculates that 3% of the films released are flops. If the manager...

A film distribution manager calculates that 3% of the films released are flops.

If the manager is correct, what is the probability that the proportion of flops in a sample of 752 released films would be greater than 4%? Round your answer to four decimal places.

Solutions

Expert Solution

Proportion of films released are flops: p = 3/100 = 0.03

Sample size : n= 752

Sample proportion $\widehat{p}$ follows normal distribution with mean $\mu _{\widehat{p}}$ = p = 0.03 and standard deviation $\sigma _{\widehat{p}}=\sqrt{p(1-p)/n}=\sqrt{0.03(1-0.03)/752}=0.0062$

probability that the proportion of flops in a sample of 752 released films would be greater than 4% = $P(\widehat{p} > 0.04)$

$P(\widehat{p} > 0.04)=1-P(\widehat{p}\leq 0.04)$

Z-score for 0.04 = (0.04 - $\mu _{\widehat{p}}$ ) / $\sigma _{\widehat{p}}$ = (0.04-0.03)/0.0062 = 1.61

From standard normal tables,

P(Z $\leq$ 1.61) = 0.9463

$P(\widehat{p}\leq 0.04)=P(Z\leq 1.61)=0.9463$

$P(\widehat{p} > 0.04)=1-P(\widehat{p}\leq 0.04)=1-0.9463=0.0537$

probability that the proportion of flops in a sample of 752 released films would be greater than 4% = 0.0537

orchestra answered 1 year ago

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