Answer:
To find the probability distribution for the number of courses taken by a randomly sampled student, we need to calculate the probabilities for each possible value of X (the number of courses taken). Let's denote P(X = x) as the probability that a student is taking x courses.
You mentioned the following counts:
300 students are taking one course (X = 1).
200 students are taking two courses (X = 2).
150 students are taking three courses (X = 3).
100 students are taking four courses (X = 4).
50 students are taking five courses (X = 5).
20 students are taking six courses (X = 6).
To calculate the probability of a student taking a specific number of courses (P(X = x)), divide the number of students taking that number of courses by the total number of undergraduates.
The total number of undergraduates is:
Total = 300 + 200 + 150 + 100 + 50 + 20 = 820
Now, calculate the probabilities:
P(X = 1) = 300 / 820
P(X = 2) = 200 / 820
P(X = 3) = 150 / 820
P(X = 4) = 100 / 820
P(X = 5) = 50 / 820
P(X = 6) = 20 / 820
Now, calculate these probabilities:
P(X = 1) = 0.3659 (rounded to four decimal places)
P(X = 2) = 0.2439 (rounded to four decimal places)
P(X = 3) = 0.1829 (rounded to four decimal places)
P(X = 4) = 0.1219 (rounded to four decimal places)
P(X = 5) = 0.0609 (rounded to four decimal places)
P(X = 6) = 0.0244 (rounded to four decimal places)
So, the probability distribution of the number of courses taken by a randomly sampled student is as follows:
P(X = 1) ≈ 0.3659
P(X = 2) ≈ 0.2439
P(X = 3) ≈ 0.1829
P(X = 4) ≈ 0.1219
P(X = 5) ≈ 0.0609
P(X = 6) ≈ 0.0244
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