(show your work for full credit)

1. (0.25 points) A national study found that 44% of college students engage in binge drinking (5 drinks at a sitting for men, 4 for women). A professor surveyed a random sample of 244 students at his college.

What is the probability that less than 96 of them admitted to binge drinking?

2. Suppose the weights of college textbooks are normally distributed with a population mean of 4 pounds and a population standard deviation of 1.2 pounds. Suppose randomly sample and weigh 16 textbooks. Answer the following questions:

a. (0.25 points) What is the probability that the sample average of the 16 textbooks is less than 3.5 pounds? (use 2 decimal places in your answer))

b. (0.25 points) What is the probability that a given (i.e. one) textbook weighs more than 5.5 pounds? (use 2 decimal places in your answer)

c. (0.25 points) Imagine the distribution of all possible samples averages of textbook weights (with n=16). What is the weight that separates the lightest 25% of sample averages from the heaviest 75% of sample averages? (round your answer to the nearest tenth of a pound)