Problem 3 (20 points) The marks on a statistics midterm test are normally distributed with a mean of 75 and a standard deviation of 4. a. What proportion of the class has a midterm test mark that is less than 80? Round your answer up to the nearest percentage point. Show your work. (4 points) 9 b. What is the probability that a class of 16 has an average midterm test mark that is less than 80? Make sure to show the mean, standard deviation, and shape of the distribution as part of your answer. Show your work. (6 points) c. What is the probability that a class of 50 has an average midterm test mark that is less than 80? Make sure to show the mean, standard 16 deviation, and shape of the distribution as part of your answer. Show your work. (6 points) 36 d. What is the probability that in a random sample of 10 students, more than 4 students have midterm test mark that is less than 80? Show ong your work. (4 points)