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(d) What is the approximate probability that the grade point average for 25 randomly chosen Math 118 students is B or better, P(x > 3)?

(d) What is the approximate probability that the grade point average for 25 randomly chosen Math 118 students is B or better, P(x > 3)?

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
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**5.24 Grades in a math course.** Indiana University posts the grade distributions for its courses online. In one spring semester, students in Math 118 received 16.1% A’s, 34.3% B’s, 29.2% C’s, 9.6% D’s, and 9.8% F’s. (a) Using the common scale A = 4, B = 3, C = 2, D = 1, F = 0, take X to be the grade of a randomly chosen Math 118 student. Use the definitions of the mean (page 237) and standard deviation (page 245) for discrete random variables to find the mean μ and the standard deviation σ of grades in this section. (b) Math 118 is a large enough course that we can take the grades of an SRS of 25 students and not worry about the finite population correction factor. If x̄ is the average of these 25 grades, what are the mean and standard deviation of x̄? (c) What is the probability that a randomly chosen Math 118 student gets a B or better, P(X ≥ 3)? (d) What is the approximate probability that the grade point average for 25 randomly chosen Math 118 students is B or better, P(x̄ ≥ 3)? (e) Explain why the probabilities in parts (c) and (d) are so different.
Transcribed Image Text:**5.24 Grades in a math course.** Indiana University posts the grade distributions for its courses online. In one spring semester, students in Math 118 received 16.1% A’s, 34.3% B’s, 29.2% C’s, 9.6% D’s, and 9.8% F’s. (a) Using the common scale A = 4, B = 3, C = 2, D = 1, F = 0, take X to be the grade of a randomly chosen Math 118 student. Use the definitions of the mean (page 237) and standard deviation (page 245) for discrete random variables to find the mean μ and the standard deviation σ of grades in this section. (b) Math 118 is a large enough course that we can take the grades of an SRS of 25 students and not worry about the finite population correction factor. If x̄ is the average of these 25 grades, what are the mean and standard deviation of x̄? (c) What is the probability that a randomly chosen Math 118 student gets a B or better, P(X ≥ 3)? (d) What is the approximate probability that the grade point average for 25 randomly chosen Math 118 students is B or better, P(x̄ ≥ 3)? (e) Explain why the probabilities in parts (c) and (d) are so different.
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