Suppose $80 \%$ Of the Incoming Email Messages for a College's Computer System

Suppose $80 \%$ of the incoming email messages for a college's computer system are spam.
-Would your answer "Because you are considering a large sample size, the Central Limit Theorem predicts the sampling distribution of sample proportions of messages that are spam is approximately normal, centered at 80 with standard deviation $\sqrt{.8(.2) / 200}$ or .0283 . So the $z$ -score for a proportion of .75 equals $(.75-.8) / .0461$ or -1.77 . The probability lying to the right (exceeding .75) equals .9616." be larger, smaller, or the same if the sample size were 100 messages rather than 200 messages? Explain briefly.

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