1) Some researchers are interested in the GPA difference between freshmen and sophomores. The distributions of GPAs in both groups are approximately normal. From previous school records, we know that the mean is 3.5 and standard deviation is 0.5 for freshmen. the mean is 3.2 and standard deviation is 0.8 for sophomores. Independent random samples of 40 students are to be selected from both years ( for a total of 80 students).

1-1) If the sample mean GPA is to be calculated for both groups and we calculated the difference between freshmen and sophomores, what is the expected value for the difference in sample means?

1-2) If the sample mean GPA is to be calculated for both groups and we calculate the difference between freshmen and sophomores, what is the standard deviation of the sampling distribution of the difference in sample means?

1-3) what is the probability that the average GPA in freshmen is higher than the average GPA in the sample of sophomores?

1-4) what is the probability that the average GPAs in the two samples differs by no more than 0.2?