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 14 such institutions. We are interested in the number that offer distance learning courses.

Part (a) In words, define the Random Variable X.

1. the number of distance learning courses offered at each college or university

2. the percentage of colleges and universities that offer distance learning courses

3. the number of colleges and universities that offer distance learning courses

4. the number of colleges and universities in the United States

Part (b) List the values that X may take on.

1. X = 1, 2, 3, . . ., 95, 96

2. X = 1, 2, 3, . . ., 12, 13, 14

3. X = 0, 1, 2, . . ., 12, 13, 14

4. X = 0, 1, 2, 3, . . ., 95, 96

Part c. Give the distribution of X. (Enter exact numbers as integers, fractions, or decimals.)

X ~ ? ( , )

Part d. On average, how many schools would you expect to offer such courses? (Round your answer to the nearest whole number.)
schools

Part e. Find the probability that at most twelve offer such courses. (Round your answer to four decimal places.)

part f. Is it more likely that 13 or that 14 will offer such courses? Use numbers to justify your answer numerically and answer in a complete sentence.

The probability that 13 schools will offer such courses is ---Select--- 0.0892 0.3294 0.5647 0.6706 or 0.9108 and the probability that 14 schools will offer such courses is ---Select--- 0.0892 0.3294 0.5647 0.6706 or 0.9108 . Therefore, it is more likely that ---Select--- 13 or 14 schools will offer distance learning courses.