Question

A. To compute a student's Grade Point Average (GPA) for a term, the student's grades for each course are weighted by the number of credits for the course. Suppose a student had these grades:
3.6 in a 5 credit Math course
2.2 in a 2 credit Music course
2.6 in a 5 credit Chemistry course
3.1 in a 4 credit Journalism course
What is the student's GPA for that term? Round to two decimal places.

B) For a 4-unit class like Statistics, students should spend average of 12 hours studying for the class. A survey was done on 23 students, and the distribution of total study hours per week is bell-shaped with a mean of 13 hours and a standard deviation of 2.8 hours.

Use the Empirical Rule to answer the following questions.

i) 68% of the students spend between__hours and__hours on Statistics each week.

ii) 95% of the students spend between__hours and__hours on Statistics each week.

iii) 99.7% of the students spend between__hours and__hours on Statistics each week.

Answer 1

a) Total credit = 5 + 2 + 5 + 4 = 16

GPA = (3.6 * 5 + 2.2 * 2 + 2.6 * 5 + 3.1 * 4) / 16 = 2.99

b) According to empirical rule 68%, 95% and 99.7% of the area lies within 1, 2 and 3 standard deviations from the mean respectively.

i) 13 - 2.8 = 10.2

13 + 2.8 = 15.8

68% of the students spend between_10.2_hours and_15.8_hours on Statistics each week.

ii) 13 - 2 * 2.8 = 7.4

13 + 2 * 2.8 = 18.6

95% of the students spend between_7.4_hours and_18.6_hours on Statistics each week.

iii) 13 - 3 * 2.8 = 4.6

13 + 3 * 2.8 = 21.4

99.7% of the students spend between_4.6_hours and_21.4_hours on Statistics each week.