Women can get breast implants, done for reconstructive purposes after mastectomy

Question

Women can get breast implants, done for reconstructive purposes after mastectomy for breast cancer, or other reason, or just for cosmetic reasons. A plastic surgeonis office purchased a very large batch of silicon breast implants from a vendor theyive never used before. They decide to test random samples of size n to see if they meet the required specification. They computed 90% confidence intervals for each random sample drawn, in order to estimate the true proportion of implants in the batch that meet specification.

(a) Based on repeated independent simple random samples of size 5 drawn from the population batch of breast implants, what is the probability that at most three of the computed confidence intervals will contain the true population proportion of implants that meet specification.

(b) Based on repeated independent simple random samples of size 100 drawn from the population batch of breast implants, what is the probability that at least 84 of the computed confidence intervals will contain the true population proportion of implants that meet specification.

Explanation / Answer

A) Total sample of size 5=n

Atleast three three of the computed confidence intervals will contain the true population proportion =3/n

B) Total sample of size 100=n

Atleast 84 of the computed confidence intervals will contain the true population proportion =84/n

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