Question

An epidemiologist is planning a study on the prevalence of oral contracep- tive use in a certain population. She plans to choose a random sample of n women and to sue the sample proportion of oral contraceptive users (pˆ) as an estimate of the population proportion (p). Suppose that in fact p = 0.12. Use the normal approximation (with continuity correction) to determine the probability that pˆ will be within ±0.03 of p if
(a) n = 100; (b) n = 200.