Respuesta :
Answer:
0.66% probability that exactly 40 of the murders were Cleared.
Step-by-step explanation:
For each murder, there are only two possible outcomes. Either it was cleared, or it was not cleared. The probability of a murder being cleared is independent of other murders. 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.
64% of murders committed last year were cleared by arrest or exceptional means.
This means that [tex]p = 0.64[/tex]
Fifty murders committed last year are randomly selected.
This means that [tex]n = 50[/tex]
Find the probability that exactly 40 of the murders were Cleared.
This is P(X = 40).
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 40) = C_{50,40}.(0.64)^{40}.(0.36)^{10} = 0.0066[/tex]
0.66% probability that exactly 40 of the murders were Cleared.
