At a certain college, 6% of all students come from outside the united states. incoming students there are assigned at random to freshman dorms, where students live in residential clusters of 40 freshmen sharing a common lounge area. how many international students would you expect to find in a typical cluster? with what standard deviation?

Using the binomial distribution, it is found that you would expect to find 2.4 international students in a typical cluster, with a standard deviation of 1.5 students.

For each student, there are only two possible outcomes, either they come from outside the United States, or they do not. The probability of an student coming from outside the United States is independent of any other student, which means that the binomial distribution is used.

Binomial probability distribution

Probability of x successes on n repeated trials, with p probability.

The expected value is given by:

[tex]E(X) = np[/tex]

The standard deviation is given by:

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

In this problem:

6% of students come from outside the US, thus [tex]p = 0.06[/tex].
Samples of 40 students, thus [tex]n = 40[/tex].

The expected value is:

[tex]E(X) = np = 40(0.06) = 2.4[/tex]

The standard deviation is:

[tex]\sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{40(0.06)(0.94)} = 1.5[/tex]

You would expect to find 2.4 international students in a typical cluster, with a standard deviation of 1.5 students.

A similar problem is given at https://brainly.com/question/15204050