Problem 1 Suppose the average casino patron in Las Vegas loses $110 per day, with a standard deviation of $700. Assume winnings/losses are normally distributed. a. What is the probability that a random group of nine people averages more than $500 in winnings on their one-day trip to Las Vegas? b. What is the probability that a random group of nine people averages more than $500 in losses on their one-day trip to Las Vegas? Problem 2 A book publisher knows that it takes an average of nine business days from when the material for the book is finalized until the first edition is printed and ready to sell. Suppose the exact amount of time has a standard deviation of four days. a. Suppose the publisher examines the printing time for a sample of 36 books. What is the probability that the sample mean time is shorter than eight days? b. Suppose the publisher examines the printing time for a sample of 36 books. What is the probability that the sample mean time is between 7 and 10 days? c. Suppose the publisher signs a contract for the printer to print 100 books. If the average printing time for the 100 books is longer than 9.3 days, the printer must pay a penalty. What is the probability the penalty clause will be activated? d. Suppose the publisher signs a contract for the printer to print 10 books. If the average printing time for the 10 books is longer than 9.7 days, the printer must pay a penalty. What is the probability the penalty clause will be activated? Problem 3 The Department of Education wishes to estimate the average SAT score among U.S. high school students. How many students would they have to sample, given that the test has a known population standard deviation of 100, in order to ensure that the margin of error was no more than 20 for a 99% confidence interval? Problem 4 Each portion of the SAT exam is designed to be normally distributed such that it has a population standard deviation of 100 and a mean of 500. However, the mean has changed over the years as less selective schools began requiring the SAT, and because students later began to prepare more specifically for the exam. Construct a 90% confidence interval for the population mean from the following eight scores from the math portion, using the population standard deviation of 100: 450, 660, 760, 540, 420, 430, 640, and 580