Salem College is embarking on a capital expenditure program involving a new campus building that depends on projected enrollment. There is a 60 percent chance that enrollment will increase by 1,000 students and a 40 percent chance that enrollment will increase by 500 students. If the current enrollment is 7,000 students, what should the design capacity of the new campus building be?
A) 800 students
B) 6,200 students
C) 7,800 students
D) 8,500 students

Question

Quizplus · Accepted Answer

To determine the design capacity of the new campus building, we need to calculate the expected value of the enrollment increase.

Expected value = (probability of enrollment increase by 1,000 students x increase in enrollment by 1,000 students) + (probability of enrollment increase by 500 students x increase in enrollment by 500 students)

Expected value = (0.6 x 1,000) + (0.4 x 500) = 760

Therefore, the expected increase in enrollment is 760 students.

To determine the design capacity, we need to add the expected increase in enrollment to the current enrollment of 7,000 students.

Design Capacity = Current Enrollment + Expected Increase

Design Capacity = 7,000 + 760 = 7,760 students

Therefore, the design capacity of the new campus building should be 7,800 students, which is closest to option C.

Salem College Is Embarking on a Capital Expenditure Program Involving