Question

Use the following scenario and data for all the questions
Among the N=16 students taking a graduate statistics class, A=10are master students and the other N-A=6 are doctorial students. A random sample of n=5 students is going to be selected to work on a class project. Use Xto denote the number of master students in the sample. Keep at least 4 decimal digits if the result has more decimal digits.

1. The probability that exactly 4 master students are in the sample closest to

2. the probability that all 5 students in the sample are master students closest to

3. the probability that at least 4 students in the sample are master students closest to

4. the probability that at most 3 students in the sample are master students closest to

Answer 1

This is a hypergeometric distribution

N = 16

A = 10

n = 5

a) P(X = 4) = 10C4 * 6C1 / 16C5 = 0.2885

b) P(X = 5) = 10C5 / 16C5 = 0.0577

c) P(X > 4) = P(X = 4) + P(X = 5)

                  = 10C4 * 6C1 / 16C5 + 10C5 / 16C5

                  = 0.3462

d) P(X < 3) = 1 - P(X > 4) = 1 - 0.3462 = 0.6538