Question

A bottle maker believes that 12% of his bottles are defective. If the bottle maker is correct, what is the probability that the proportion of defective bottles in a sample of 635 bottles would be less than 11%? Round your answer to four decimal places.

Answer 1

The proportion of defectives is p 0.12 The sample size is n = The mean of the sampling distribution is u=p = 0.12 635 The variance of the sampling distribution is g' = P(1-p) n Compute the probability that the proportion of defective bottles in a sample of 635 bottles would be less than 11%. That is, 0.11-0.12 P(<0.11) P (convert to z-score) 0.12x 0.88 Pq 635 from standard normal tables) -P(Z<-0.775)- P(Z <-0.78) =0.2177 Therefore, the probability that the proportion of defective bottles in a sample of 635 bottles would be less than 11% is |0.2177.