There are 5000 undergraduates registered at a certain college. Of them, 448 are taking one course, are taking two courses, 675 are taking three courses, are taking four courses, are taking five courses, and are taking six courses. Let be the number of courses taken by a student randomly sampled from this population. Find the probability distribution of . Round the answers to four decimal places as needed.

Step-by-step explanation:

Hello!

There are some values missing, so I'll find the probability distribution using others as example. Afterwards you can calculate the ones corresponding to this exercise following the same steps.

Considering there are 5000 undergraduates registered in the college.

465 are taking one course

658 are taking two courses

566 are taking three courses

1877 are taking four courses

1344 are taking five courses

90 are taking six courses

First you have to define the variable of interest. To identify it you have to ask yourself the following question: what is the characteristic of this population that is being measured?

The answer is "the number of courses an undergraduate is taking" and this will be the study variable X

X can take values from 1 to 6 courses.

To calculate the probability of each value of X, you have to divide the "number of students taking Xi courses" by "total number of students registered in the college"

For

X=1

P(1)= 465/5000= 0.093

X=2

P(2)= 658/5000= 0.1316

X=3

P(3)= 566/5000= 0.1132

X=4

P(4)= 1877/5000= 0.3754

X=5

P(5)= 1344/5000= 0.2688

X=6

P(6)= 90/5000= 0.018

For this to be a probability distribution the following condition should be met:

F(X)= ∑P(X) = 1

In this example: 0.093 + 0.1316 + 0.1132 + 0.3754 + 0.2688 + 0.018 = 1

I hope this helps!