MAT143-Lab 4 - Probability

MAT143 Lab 4 Central Piedmont Community College Part 1 Many say that baseball is a game with low success rate. Consider Mookie Betts, one of the greatest players the sport has ever seen. He had a batting average (BA) of .346 during the 2018 season. His batting average was the highest of all players for that year. A player’s batting average is computed by dividing the number of times a player has a hit by the player’s total number of at-bats. 𝐵𝐴 = 𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝐻𝑖𝑡𝑠 𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝐴𝑡−𝐵𝑎𝑡𝑠 Notice that this formula looks a lot like a probability where the sample space is the set of all at-bats and the event is getting a hit. When fans talk about batting averages, they commonly think of it in terms of probability. That is, if a player is batting, .250, then there is a 25% chance that they will be a hit at their next at-bat. 1. Do you agree with the interpretation of the batting average as a probability? Is it possible to compute the theoretical probability that a player will get a hit when at bat? Explain you answer. Many factors go into whether or not you will hit the ball. But overall I think that it is possible to compute the theoretical probability because you are finding the probability of the number of favorable outcomes (hitting the ball) over the number of possible outcomes. This is all determined by sample space. 2. Let’s return our attention to Mookie Betts. Betts had 520 at-bats during the 2018 season; how many hits did he have that season? Round your answer to the nearest whole number. 520 x 0.346 = 180 hits 3. Suppose that Mookie Betts had another 20 at-bats during the 2018 season. Assume he had a BA of .500 for those 20 at-bats. What would his new batting average be with these extra 20 at-bats? 190 x 0.352 = 190 hits .352 would be his new batting average with 190 hits. Part 2 Suppose two competitive friends, Student A and Student B are both finishing up a course on technical writing at different colleges. At the end of the semester, they compare their grades to see who did better in this course. Each friend had to complete a different number of graded assignments and exams where each grade was given equal weight. The grades earned by the two students on all graded assignments and exams are as follows. Student A: 78, 89, 95, 69, 98, 0, 87, 84, 76, 93, 89, 77, 75 Student B: 87, 79, 88, 91, 89, 77, 86, 93, 105, 89 1. For each set of grades, determine the mean, median, mode, and range. Round answers to the nearest tenth, if necessary. Comparison of Students’ Grades Student A Student B Mean 76.23 88.4 Median 84 88.5 Mode 89 89 Range 98 28 2. Compare the grades of the two students. Which value(s) did you use in your comparison? Explain your reasoning. By comparing the grades of two student , the student B grades is better than student A because all the statistical measure are good for student b as compared to A 3. Determine which value(s) in each student’s grades are outliers and remove the outlier(s) from the data sets. Explain why each data point you removed is an outlier. 0,61,64,76,77, These were removed from the data sets because they drastically altered the data information. 4. For the modified data set, determine the mean, median, mode, and range again. Round the answers to the nearest tenth, if necessary. Comparison of Students’ Grades with Outliers Removed Student A Student B Mean 82.58 87.75 Median 88.5 88.5 Mode 89 89 Range 37 14 5. Do these new values change your mind of which student performed better in the technical writing course? Explain why or why not? These values do change how I think because the median is now tied with student A when it was not before. 6. Do you think outliers should be removed when comparing grades between students? Explain your reasoning. I do not believe outliers should be removed because I feel like it is not getting the correct data if you do not include them.