Suppose 80% of the incoming email messages for a college’s computer system are spam. 1. Use the CLT to approximate the probability that in a random sample of 200 incoming email messages at this college, the sample proportion of these messages that are spam would exceed .75. 2. Display your answer to question 1 as a shaded area in a well-labeled sketch. 3. After implementing a new spam blocker, if it turns out that a random sample of 200 messages contains 75% spam, would this constitute fairly convincing evidence that the (population) percentage of spam has been reduced from 80%?Explain, based on your calculation in question 1. 4. Would your answer to question 1 be larger, smaller, or the same if the sample size were 100 messages rather than 200 messages? Explain briefly. 5. Would your answer to question 1 be larger, smaller, or the same if the (population) proportion of spam messages were .77 rather than .80? Explain briefly.
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