Question

More than 96 percent of the very largest colleges and universities (more than 15,000 total enrollments) have some online offerings. Suppose you randomly pick 13 such institutions. We are interested in the number that offer distance learning courses.

a. X can take any value between 0 and 13, inclusive.
b. X can only take values from 0 to 4, inclusive.
c. X can take values from 5 to 9, inclusive.
d. X can take values from 10 to 13, inclusive.

Answer 1

The question is about the number of colleges and universities that offer distance learning courses out of a randomly selected group of 13 institutions. The correct option is a. X can take any value between 0 and 13, inclusive.

Step-by-step explanation:

The subject of this question is mathematics and the grade level is college. The question is asking about the number of colleges and universities that offer distance learning courses out of a randomly selected group of 13 institutions.

To answer this question, we need to use the binomial distribution. Let X represent the number of institutions that offer distance learning courses. With a success rate of 96% and a sample size of 13, we can model X as a binomial random variable with parameters n = 13 and p = 0.96.

We can find the probabilities of X taking different values using the binomial probability formula. X can take any value between 0 and 13, inclusive, so the correct option is a. X can take values from 5 to 9, inclusive, so option c is incorrect. X cannot take values from 10 to 13, inclusive, so option d is also incorrect. The correct answer is option a.