10 12 13 15 16 18 Mat 170-703 Name: Project #3 - 100 points (10 point per day penalty if late) Spring 2022 - Due Thursday, April 21st . Problem: A statistics professor gives an exam that is worth a maximum of 50 points. The teacher knows from past experience that the test scores are normally distributed with a mean score of 33 and a standard deviation of 5.5 The original grade scale is 45-50 is an A; 40-44 is a B; 35-39 is a C; 30-34 is a D; and 29 or less is an F. Since this exam was particularly tough, the teacher decides to curve the test scores. Questions: If the professor simply adds 5 points to everyone's test score, what is the new mean? What is the new standard deviation? This question has nothing to do with the rest of the project! You are to answer it but not use it anywhere else!! If the grades are curved using the following parameters (instead of simply adding more points to each test), find the numerical limits for each letter grade. Round each new value in the grade scale to the nearest whole number. A: Top 10% (also known as the 90 percentile) B: Scores above the bottom 70% and below the top 10% (the 70th "percentile) C: Scores above the bottom 30% and below the top 30% (the 30thp "percentile) D: Scores above the bottom 10% and below the top 70% (the 10" percentile) F: Bottom 10% Using the teacher's original grade scale, if one student is selected at random, what is the probability that the test score is a 'B' or higher? Remember that the exam has a maximum possible 50 points. What is the probability of getting 'B' or higher when you select one student at random using the 'new' grade scale from #2? Remember that the exam has a maximum possible 50 points.10 12 13 15 16 18 Using the original grade scale and selecting 6 students at random, what is the probability that their mean score would be an 'A'? Can the Central Limit Theorem be used in this case even though the sample is small? Why? In an attempt to get an estimate of the proportion of his students that generally pass his exam; the statistics professor takes a sample of his data from past classes. He finds that in a sample of 200 test scores, 135 students got a passing grade. He then calculated the following 95% confidence interval estimate based on this sample: 61%