There are 4,000 undergraduates registered at a certain college. Of them, 364 are taking one course, 496 are taking two courses, 460 are taking three courses, 1,512 are taking four courses, 1,056 are taking five courses, and 112 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.

X=1, P = 0.091

X=2, P = 0.124

X=3, P = 0.115

X=4, P = 0.378

X=5, P = 0.264

X=6, P = 0.028

Step-by-step explanation:

To calculate the probability distribution of X, first we have to define the sample space.

In this case X=1,2,3,4,5,6. This are the values that X can take.

The probability is calculated as equal to the relative frequency of each of the values.

For X=1, P = 364/4000 = 0.091

For X=2, P = 496/4000 = 0.124

For X=3, P = 460/4000 = 0.115

For X=4, P = 1512/4000 = 0.378

For X=5, P = 1056/4000 = 0.264

For X=6, P = 112/4000 = 0.028