Scenario 1: We spent $20,000 on a digital campaign targeting “STEM Interest” students. Historically, the application rate for our general inquiry pool is 10%. We had 5,000 students in the STEM campaign. 600 of them applied.  We want to know if the campaign actually influenced behavior or if these students would have applied anyway. Using conditional probability, determine if the campaign worked.

Scenario 2: The President wants a precise forecast for the incoming class size. We cannot use a single yield rate because Locals (1,000 admits, historic yield is 30%) and Out-of-State students (2,000 admits and historic yield is 10%) behave differently. Using the Law of Total Probability, what is the total expected size of the incoming class?

Scenario 3: We have admitted 2,500 students. Our historical yield rate is 20%. We have exactly 525 beds in the residence halls. Do we risk overfilling the 525 beds?

Scenario 4: During the week before the deposit deadline, we expect a surge in phone calls. Historical data shows we average 16 calls per hour. We want to staff enough student workers to handle “Peak Volume.” How many calls per hour should we staff for?