Respuesta :
Answer:
0.4875
Step-by-step explanation:
For each student, there are only two possible outcomes. Either they are a graduate student, or they are not. The probability of a student being a graduate student is independent from other students. So we use the binomial probability distribution to solve this question.
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 combinations 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.
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.
This means that [tex]n = 5[/tex]
Determine the probability that the sample contains fewer than two graduate students?
[tex]P(X < 2) = P(X = 0) + P(X = 1)[/tex]
In which
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{5,0}.(0.32)^{0}.(0.68)^{5} = 0.1454[/tex]
[tex]P(X = 1) = C_{5,1}.(0.32)^{1}.(0.68)^{4} = 0.3421[/tex]
[tex]P(X < 2) = P(X = 0) + P(X = 1) = 0.1454 + 0.3421 = 0.4875[/tex]
0.4875 = 48.75% probability that the sample contains fewer than two graduate students
