Assume 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.
Answer: P(X >0.75) = P{ z > (0.75 - 0.80) / square root[0.80(1-0.80) / 200] } = P( z > -1.768 )
Using the standard normal tables P( z > -1.768 ) = 0.9615
2. 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.