1. In a recent survey of college professors, it was found that the average amount of money spent on entertainment each week was normally distributed with a mean of $95.25 and a standard deviation of $27.32. What is the probability that the average spending of a sample of 25 randomly-selected professors will exceed $102.50?
2. The number of students using the ATM on campus daily is normally distributed with a mean of 237.6 and a standard deviation of 26.3. For a random sample of 55 days, what is the probability that ATM usage averaged more than 230 students per day?
3. In examining the invoices issued by a company, an auditor finds that the dollar amounts of invoices have a mean of $1,732 and a standard deviation of $298. What is the probability that for a sample of 45 invoices, the average is greater than $1,800?
