Question

A film distribution manager calculates that 5% of the films released are flops.

If the manager is correct, what is the probability that the proportion of flops in a sample of 455 released films would differ from the population proportion by greater than 3%? Round your answer to four decimal places.

Answer 1

for normal distribution z score =(p̂-p)/σp
here population proportion=     p=	0.0500
sample size       =n=	455
std error of proportion=σp=√(p*(1-p)/n)=	0.0102

probability that the proportion of flops in a sample of 455 released films would differ from the population proportion by greater than 3%:

probability =1-P(0.02<X<0.08)=1-P((0.02-0.05)/0.01)<Z<(0.08-0.05)/0.01)=1-P(-2.94<Z<2.94)=1-(0.9984-0.0016)=0.0032