Suppose you are sampling from a large population, and you ask the respondents whether they believe men should be allowed to take paid paternity leave from their jobs when they have a new child. Each person you sample is equally likely to be male or female. The population proportion of females who believe males should be granted paid paternity leave is 56%, and the population proportion of males who favor it is 48%. If you sample 200 people and count the numbers who believe males should be granted paternity leave, is this number binomially distributed? Explain why or why not. Would your answer change if you knew your sample was going to consist of exactly 100 males and 100 females?
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