What is the probability that two groups of students selected

What is the probability that two groups of students selected at random, consisting of 32 and 50 students, respectively, will differ in their mean scores by more than 20 points?

Pls show all work

(Two Sample Means) the mean score for freshmen on an aptitude test at a certain college is 690,with a standard deviation of 50. What is the probability that two groups of students selected at random, consisting of 32 and 50 students, respectively, will differ in their mean scores by more than 20 points? What is the probability that two groups of students selected at random, consisting of 32 and 50 students, respectively, will differ in their mean scores by more than 20 points? Pls show all work

Solution

The mean score of the 32 students is denoted by Xbar and of the 50 students
is denoted by Xbar then the mean of (Xbar -Ybar)= (690-690)=0
Variance (Xbar-Ybar) =50