Question

A researcher reports that the probability of a college student living on campus is p = .38. If a small local college has 2,000 students enrolled, then what is the standard deviation of college students living on campus? Hint: This is a binomial probability distribution.

Answer 1

Answer:

The standard deviation of the distribution is 21.7 students.

Step-by-step explanation:

We are given the following in the question:

We treat college student living on campus as a success.

P(college student living on campus) = 0.38

Then the number of students follows a binomial distribution.

Sample size, n = 2000

We have to evaluate the standard deviation of the distribution.

Formula:

$\sigma = \sqrt{np(1-p)}$

Putting values, we get,

$\sigma = \sqrt{2000(0.38)(1-0.38)} = 21.7$

Thus, the standard deviation of the distribution is 21.7 students.