) 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

-2x + 7 = 7

subtract 7 from both sides.

-2x = 0

divide both sides by -2.

x = 0

ca = ec

cpctc makes it so that corresponding parts of the triangle you proved to be equal are equal, the other options aren't part of the part of the triangles you proved to be equal.