Question

There are 5000 undergraduates registered at a certain college. Of them, 493 are taking one course, 630 are taking two courses, 570 are taking three courses, 1849 are taking four courses, 1372 are taking five courses, and 86 are taking six courses. Let X be the number of courses taken by a student randomly sampled from this population. Find the probability distribution of X. Round the answers to four decimal places as needed. x .....4 5 6 ..P(x). ........

Answer 1

The probability distribution of X, the number of courses taken by a student, is calculated by dividing the number of students enrolled in each course amount by the total number of students. This gives a set of probabilities for the values of X that can be rounded to four decimal places.

Step-by-step explanation:

To find the probability distribution of X, the number of courses taken by a student randomly sampled from the given population of undergraduates, we first need to understand that a probability distribution assigns a probability to each possible value that the random variable can take on. In this case, X can take on values {1, 2, 3, 4, 5, 6}, corresponding to the number of courses taken.

The probability of each value of X is calculated as the number of students taking that many courses divided by the total number of students. Here are the calculations:

• P(X=1) = 493 / 5000 = 0.0986
• P(X=2) = 630 / 5000 = 0.1260
• P(X=3) = 570 / 5000 = 0.1140
• P(X=4) = 1849 / 5000 = 0.3698
• P(X=5) = 1372 / 5000 = 0.2744
• P(X=6) = 86 / 5000 = 0.0172

These probabilities can be rounded to four decimal places as needed.