University admissions

Suppose a university announced that it admitted \({{ params.description.num1 }}\) students for the following year’s freshman class. However, the university has dorm room spots for only \({{ params.description.num2 }}\) freshman students.

If there is a \({{ params.description.num3 }}\)% chance that an admitted student will decide to accept the offer and attend this university, what is the approximate probability that the university will not have enough dormitory room spots for the freshman class? .

Part 1

Using the normal approximation

Part 2

Using the normal approximation with the 0.5 cut-off correction

Attribution

Problem is from the OpenIntro Statistics textbook, licensed under the CC-BY 4.0 license.