Mat 152 Project 4 The Central Limit Theorem Student Learning Outcomes: 1) The student will demonstrate and compare properties of the central limit theorem. The Data A central tenet to being a good instructor, I believe, is to be a reflective practitioner of your craft. From time to time I find it to be necessary to review and reflect on my work as an instructor from a grade perspective. On our moodle page you will find a link to a second word document titled '300 Grades". This data sheet contains both the alphanumeric grade (page 1) and the numerical equivalent (page 2) for every grade I have given for the last 300 students that have attempted this very course. After your readings in chapter 7 and examining this 300 grades document, it should be relatively obvious that it is not uncommon to find an individual student that would achieve an A in my class. However, logically, it would be much more difficult to find a FULL CLASS (25 students) that would achieve an A average for my course. This project will help us answer this question... together. Objective 1 (28 points) Using excel or statcato, stack all ten columns together into a single column. Once you have all 300 grades in a single column, calculate: 1) The average numeric grade for all 300 students 2) The standard deviation for numeric grade for all 300 students 3) If we were to assume the population of grades was normally distributed (which it certainly isn't) calculated the probability that an individual would have a final grade higher than a 90. 4) Again, assuming normality, calculate the probability that an individual was have a final grade higher than 80.Objective 2 (21 points) Since we are attempting to examine the behavior of a class of students, the behavior of an individual (as we calculated in objective 1) is really of little concern to us. Assuming that there are 30 students enrolled for a typical class, use the central limit theorem to calculate the following: 1) What would be the shape of the distribution of the average class grade of these 30 students? 2) What would be the average class average of these 30 students be? 3) What would the standard deviation of the class average be for these 30 students? Objective 3 (3 points) Watch this video. Objective 4 (28 points) After watching the simulation video in objective 3, address the following questions: 1) What is the probability that a class of 30 students would have a final average grade higher than a 90? 2) Compare your results from objective 4 question 1 to your answer in objective 1 question 3. At face value, the two questions seem very similar, but you should have quite different responses. Is the probability of the 30 students higher or lower than just the individual? Why?\f95 96 94 58 57 94 89 88 97 50 94 76 61 63 78 90 79 81 86 98 91 64 92 95 85 79 89 88 95 94 92 65 40 80 93 81 95 89 91 96 88 58 88 77 98 91 97 79 93 92 94 91 61 74 90 89 80 95 96 80 91 95 90 85 77 58 98 99 100 95 97 89 85 86 71 78 88 94 72 68 97 83 88 62 89 93 42 98 89 88 59 79 95 93 80 92 96 93 89 86 96 99 93 77 59 93 89 88 92 93 88 97 80 89 93 86 95 97 93 35 68 99 94 84 58 67 93 98 88 98 88 85 84 92 80 87 95 90 93 98 93 91 89 64 96 87 91 95 96 84 89 88 97 65 97 88 79 95 92 58 75 83 95 91 92 87 89 84 89 92 60 86 87 46 91 93 95 96 98 83 93 98 83 75 97 59 93 89 47 94 86 91 92 95 88 83 87 95 88 96 93 79 85 95 78 80 81 89 97 89 89 95 94 88 68 85 83 95 84 78 89 87 98 80 93 96 88 97 82 93 43 87 54 93 95 97 93 87 94 94 92 90 95 68 83 88 93 95 89 97 93 79 87 95 97 89 96 91 98 86 86 89 56 68 91 98 64 97 96 95 89 88 85 79 95 96 94 57 99 79 95 97 96 77 75 60 87 67 63 84 95 96 91 89 93 95 69 86 61 53