Week 5 Activity (Grading on a Curve Student)

1. Suppose a professor gives an exam to a class of 40 students and the scores are as follows. ( Type the data set in StatCrunch.) 35 44 46 47 47 48 49 51 53 54 55 55 57 57 57 58 59 59 59 59 60 60 60 60 60 62 62 62 64 68 69 70 72 73 73 75 75 77 82 88 a. Find each of the following: i. Mean: 60.525 ii. Median: 59.5 iii. Standard deviation: 10.957 iv. Z -score for a student who originally scored 54 on the exam: -0.5955 b. Create a histogram of the scores and comment on the shape of the distribution. (Use a separate page if necessary.) Grading on a Curve This activity will allow you to explore a couple of different options for adjusting exam scores and the effects of each plan on the students’ results. Read the steps below and complete each item. Directions

The Histogram appears to prove that the data is normal distributed as it shows a bell- shaped curve when drawn 2. Suppose the professor wants the scores to be curved in a way that results in the following: Top 10% of scores receive an A Bottom 10% of scores receive an F Scores between the 70th and 90th percentile receive a B Scores between the 30th and 70th percentile receive a C Scores between the 10th and 30th percentile receive a D Find the range of scores that would qualify for each grade under this plan. (Assume all scores are normally distributed with a mean of 60.53 and standard deviation of 10.96.) Exam Scores Letter Grade Above 74.57 A 66.27 – 75.57 B 54.78 -- 66.27 C 46.48 – 54.78 D Below 46.48 F The workings are as below Scores above the 90th percentile receive an A p value = 0.90 z score of p-value (0.90) = 1.282 By applying normal distribution: - 1.282 = x − 60.93 10.93 x = 74.57 Scores below the 10th percentile receive an F p value = 0.10 z score of p-value (0.10) = - 1.282 By applying normal distribution: -