Question

A film distribution manager calculates that 7%of the films released are flops.

If the manager is correct, what is the probability that the proportion of flops in a sample of 653 released films would be less than 6% ? Round your answer to four decimal places.

Answer 1

Solution:

We are given

Population proportion = p = 0.07

So, q = 1 – p = 1 – 0.07 = 0.93

Sample size = n = 653

Sample proportion = P = 0.06

We have to find P(P<0.06)

Z = (P – p)/sqrt(pq/n)

Z = (0.06 – 0.07)/sqrt(0.07*0.93/653)

Z = -0.01/ 0.009985

Z = -1.0015

P(Z<-1.0015) = P(P<0.06) = 0.158292

(by using z-table/excel)

Required probability = 0.1583