Question

At a large university, 23% of students come from out-of-state. if we sample 25 students at random, what is the mean (expected number) of out-of-state students in this sample? give your answer using two decimal places.

Answer 1

The mean number of out-of-state students in a random sample of 25 students from a university with 23% of its students from out-of-state is 5.75.

Step-by-step explanation:

To calculate the mean (expected number) of out-of-state students in a sample of 25 students from a large university where 23% of students come from out-of-state, you would use the concept of the expected value for binomial distributions. The formula for the expected value (mean) is:

E(X) = n * p

Where n is the size of the sample and p is the probability of a student being from out-of-state. Here, n = 25 and p = 0.23.

Plugging in the numbers, we get:

E(X) = 25 * 0.23 = 5.75

Therefore, the mean (expected number) of out-of-state students in the sample is 5.75.

Answer 2

Multiply 25 students by 23%.
(25)(.23) = 5.75

The mean, or expected number, of out-of-state students in this sample is 5.75 students.