Refer to Exercise 49. Note that X and Y are independent random variables because the two students are randomly selected from each of the campuses. Calculate and interpret the standard deviation of the sum S = X + Y.

Exercise 49.

El Dorado Community College has a main campus in the suburbs and a downtown campus. The amount X spent on tuition by a randomly selected student at the main campus has mean $732.50 and standard deviation $103. The amount Y spent on tuition by a randomly selected student at the downtown campus has mean $825 and standard deviation $126.50. Suppose we randomly select one full-time student from each of the two campuses. Calculate and interpret the mean of the sum S = X + Y.