Question

A college wants 950 entering freshman. Experience shows that about 75% of admitted students accept. The college admits 1200 students, so if we assume decisions to enroll are made independently, the number who accept has a B(1200,0.75) distribution. What is the standard deviation of the number of students who choose to enroll

Answer 1

Given Information:

Probability of success = p = 75 %

Total number of students = n = 1200

Required Information:

Standard deviation = σ = ?

Answer:

Standard deviation = 15

Explanation:

In a binomial distribution, the probability of success does not change from trial to trial and the probability of events in not dependent on each other. Also the number of trials are fixed. So this problem can be modeled using binomial distribution.

The mean of the number of students who choose to enroll is given by

μ = n*p = 1200*0.75

μ = 900

The standard deviation of the number of students who choose to enroll is given by

σ = √np(1 - p)

σ = √1200*0.75(1 - 0.75)

σ = 15

Therefore, the standard deviation of the number of students who choose to enroll is 15.