Respuesta :
Answer:
There is a 26.29% probability that between 22 and 24 (inclusively) of them will be men.
Step-by-step explanation:
For each Pinterest user, there are only two possible outcomes. Either they are men, or they are not. So we use the binomial probability distribution to solve this problem.
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.
In this problem we have that:
Pinterest claims that 0.2788 of their app users are men. This means that [tex]p = 0.2788[/tex]
Sample of 76 users, so [tex]n = 76[/tex]
What is the probability that between 22 and 24 (inclusively) of them will be men?
[tex]P = P(X = 22) + P(X = 23) + P(X = 24)[/tex]
In which
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 22) = C_{76,22}.(0.2788)^{22}.(0.7212)^{54} = 0.0984[/tex]
[tex]P(X = 23) = C_{76,23}.(0.2788)^{23}.(0.7212)^{53} = 0.0893[/tex]
[tex]P(X = 24) = C_{76,24}.(0.2788)^{24}.(0.7212)^{52} = 0.0762[/tex]
So
[tex]P = P(X = 22) + P(X = 23) + P(X = 24) = 0.0974 + 0.0893 + 0.0762 = 0.2629[/tex]
There is a 26.29% probability that between 22 and 24 (inclusively) of them will be men.
