Respuesta :
Answer:
16.22% probability that 3 of them entered a profession closely related to their college major
Step-by-step explanation:
For each college graduate, there are only two possible outcomes. Either they have entered a profession closely related to their college major, or they have not. The probability of a college graduate having entered a profession closely related to their college major is independent of other college graduates, 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.
56% reported that they entered a profession closely related to their college major.
This means that [tex]p = 0.56[/tex]
If 8 of those survey subjects are randomly selected without replacement for a follow-up survey, what is the probability that 3 of them entered a profession closely related to their college major?
This is P(X = 3) when n = 8. So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 3) = C_{8,3}.(0.56)^{3}.(0.44)^{5} = 0.1622[/tex]
16.22% probability that 3 of them entered a profession closely related to their college major
