Imagine that proportion p = 0.82 of adults in a large city aremarried, but that this is not known, and we would like to estimatep. Suppose that we survey a random sample of 250 adults in thecity, and calculate ˆp, the sample proportion of respondents whoare married.
(a) Are the requirements met for ˆp to be approximately normallydistributed? Explain, showing any necessary calculations and/orcomputer commands.
(b) What is (approximately) the probability that ˆp will fallbetween 0.81 and 0.83? Show all calculations and/or computercommands.
(c) If we had sampled only 50 adults, would the requirements forˆp to be approximately normal still hold? Explain.
