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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.

Respuesta :

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:

[tex]\sigma = \sqrt{np(1-p)}[/tex]

Putting values, we get,

[tex]\sigma = \sqrt{2000(0.38)(1-0.38)} = 21.7[/tex]

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

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