) Thirty percent of the students in a management class are graduate students. A random sample of 3 students is selected. a) Using the binomial probability function, determine the probability that the sample contains exactly 2 graduate students. (2 pts)

Given Information:  

Probability of success = 30%

Sample size = n = 3

Variable of interest = x = 2  

Required Information:  

Probability of exactly 2 graduates = ?

Probability of exactly 2 graduates = P(2; 3, 0.30) = 0.189

Step-by-step explanation:

The given problem can be modeled as a binomial experiment since a random selected student can either b graduate or not therefore, there are only 2 outcomes. Each trial is independent and the probability of success is not changing from trial to trial. The number of trials in also fixed.

We know that a binomial distribution is given by

P(x; n, p) = nCx pˣ (1 - p)ⁿ⁻ˣ

Where p is the probability of success and 1 - p is the probability of failure, n is number of independent trials and x is the variable of interest.

For the given problem, we know that x = 2, n = 3 and p = 0.30

P(2; 3, 0.30) = 3C2*0.30²*(1 - 0.30)³⁻²

P(2; 3, 0.30) = 3*0.30²*(0.70)¹

P(2; 3, 0.30) = 0.189