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.
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
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