College admissions: A small college has enough space to enroll 290 new students

Question

College admissions: A small college has enough space to enroll 290 new students in its incoming freshman class. From past experience, the admissions office knows that 64% of students who are accepted actually enroll. If the admissions office accepts 440 students, what is the probability that there will be enough space for all the students who enroll? Use the TI-84 caleulator as needed. Round the answer to four decimal places. The probability that there will be enough space for all the students who enroll is

Explanation / Answer

We will be using binomial distribution over here and the formula would be as shown below: -

n!/x!(n-x)!*p^x*q^n-x, n=440, x=290, p=0.64, q=0.36

Hence, the probability comes out to be 0.0282

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