Question

# Use the following information for Questions 28-32. Final grades in a class are a weighted average...

Use the following information for Questions 28-32. Final grades in a class are a weighted average of the midterm (25%) and final (75%) exams: G = 0.25M + 0.75F. Each exam has 100 possible points. Suppose the average and standard deviation of scores on the midterm were 71 and 19 respectively, while the values for the final exam were 69 and 23. Suppose further that the correlation coefficient between the two exams is 0.50.

1. What is the mean of the final grades in class?

a. 65.1

b. 67.2

c. 68.6

d. 69.5

2. What is the covariance between the midterm and the final?

a. 202.5

b. 218.5

c. 223.6

d. 231.6

3. What is the variance of the final grades in class?

a. 402

b. 418

c. 423

d. 431

4. What is the standard deviation of the final grades in class?

a. 18.11

b. 19.27

c. 20.05

d. 21.93

5. Suppose the final grades are normally distributed with a mean and standard deviation found in Question 1 and Question 4. What fraction of students will get an A if they need more than 93 points to obtain that grade?

a. 0.8790

b. 0.5632

c. 0.3751

d. 0.1210

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