Use the Following Information for Questions

Multiple Choice

Use the following information for questions:
High school students can be categorized into two groups by the amount of activities they are involved in. Let group 1 consist of all high school students who are very involved in sports and other activities and group 2 consist of all high school students who aren't. The distributions of GPAs in both groups are approximately normal. The mean and standard deviation for group 1 are 2.9 and 0.4, respectively. The mean and standard deviation for group 2 are 2.7 and 0.5, respectively. Independent random samples of 50 high school students are to be selected from both groups (for a total of 100 students) .
-What is the probability that the average GPA in the sample of students who are not so involved is higher than the average GPA in the sample of students who are very involved?

A) < 0.0001
B) 0.0136
C) 0.0582
D) 0.9864