1) In a case of 36 Dannon Yogurt cups, the average amount of yogurt in each cup is supposed to be 6 ounces with a standard deviation of 1.2 ounces. What is the probability that the sample average for these 36 cups of yogurt is less than 5.5 ounces? Remember, all probabilities are taken to 4 decimal places for this class.
2) A particular professor in History with a class of 300 students decided to do a pass/fail option on the final exam. Given that the chance of passing the exam is .5, what is the probability that between 120 to 160 (do not include 120 and 160 in the interval) students failed the final exam. Use the normal approximation to the binomial to calculate this probability. Remember, all probabilities are taken to 4 decimal places for this class.