Respuesta :
Answer:
5.80% probability that exactly 1 resume will be from females.
Step-by-step explanation:
For each resume received by the corporation, there are only two possible outcomes. Either they are from a female, or they are not. The probability of a resume received being from a female is independent from other resumes. 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.
22% of all resumes received by a corporation for a management position are from females.
This means that [tex]p = 0.22[/tex]
18 resumes will be received tomorrow.
This means that [tex]n = 18[/tex]
What is the probability that exactly 1 resume will be from females?
This is P(X = 1).
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 1) = C_{18,1}.(0.22)^{1}.(0.78)^{17} = 0.0580[/tex]
5.80% probability that exactly 1 resume will be from females.
