Question

The Harvard Admission

The undergraduate admission rate at Harvard University in 2012 was 6%.

a. Assuming the admission rate is still 6%, in a sample of 100 applicants to Harvard, what is the probability that exactly 5 will be admitted? Assume that decisions to admit are independent.

b. What is the probability that exactly 95 out of 100 applicants will be rejected?

Also How would it be plugged in the calculater?

Answer 1

Let X be a random variable that denotes the number of applicants that were admitted to Harvard from a sample of 100. There are only two possible outcomes:

1) A student is admitted to Harvard - assume this to be a success. Probability of this event is given to be 0.06.

2) Student isn't admitted - assume this to be failure

Clearly the random variable X follows a binomial distribution, that is:

The probability that X students are accepted is given by :

a. We require the probability that exactly 5 students are admitted.

b. We require the probability that exactly 95 applicants are rejected. But this is equivalent to the probability that exactly 5 applicants are accepted, which we just computed.

Hope I've been of assistance. Please do provide feedback and let me know if you need any clarifications regarding the solution in the comments.