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 GPAs in the two samples differ by no more than 0.1?

A) 0.1341
B) 0.2266
C) 0.2415
D) 0.8659