a. A standardized test is given to a group of students. Test scores may range from 0 to 100. Based on statistical data from a large population, the mean test score is 80 while the most likely (mode) score is 90. What continuous probability distribution can be used to model test scores for this situation? Give parameters for the distribution.

b. The test of part a is to be given to a group of thirty students. We will average the scores to obtain a class average. What distribution approximately models the class average? What are its parameters?

c. A professor always gives tests made up of 20 short answer questions. All the questions give 5 points credit for a total score of 100 if all are answered correctly. She does give partial credit. Based on your current capability you judge that your credit on each question is a random variable with mean equal to 3 and a standard deviation equal to 1. Assume the questions are independent in terms of chance of success. Before you take the test what is your estimate of the mean and standard deviation of your test score? If a score of 80 or more earns at least a B, what is the probability that you will earn a B for this exam? You will have to make an approximation to answer this question.

d. A professor always gives tests made up of 20 short answer questions. All the questions give 5 points credit for a total score of 100 if all are answered correctly. She grades the questions as either right or wrong with no partial credit. Based on your current capability you judge that you have a 0.7 probability of answering any one question correctly. Assume the questions are independent in terms of chance of success. If a score of 80 or more earns at least a B, what is the probability that you will earn at least a B for this exam?