Respuesta :
Answer:
There is a 32.2% probability that the sample contains exactly 2 graduate students.
Step-by-step explanation:
For each student selected, there are only two possible outcomes. Either they are a graduate student, or they are not. This means that we can solve this problem using the binomial probability distribution.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinatios of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
In this problem we have that:
Thirty-two percent of the students in a management class are graduate students. This means that [tex]p = 0.32[/tex].
A random sample of 5 students is selected. What is the probability that the sample contains exactly 2 graduate students?
This is P(X = 2) when [tex]n = 5[/tex]. So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 2) = C_{5,2}.(0.32)^{2}.(0.68)^{3} = 0.3220[/tex]
There is a 32.2% probability that the sample contains exactly 2 graduate students.
