Respuesta :
Answer:
11.44% probability that exactly 12 members of the sample received a pneumococcal vaccination.
Step-by-step explanation:
For each adult, there are only two possible outcomes. Either they received a pneumococcal vaccination, or they did not. The probability of an adult receiving a pneumococcal vaccination is independent of other adults. 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.
70% of U.S. adults aged 65 and over have ever received a pneumococcal vaccination.
This means that [tex]p = 0.7[/tex]
20 adults
This means that [tex]n = 20[/tex]
Determine the probability that exactly 12 members of the sample received a pneumococcal vaccination.
This is P(X = 12).
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 12) = C_{20,12}.(0.7)^{12}.(0.3)^{8} = 0.1144[/tex]
11.44% probability that exactly 12 members of the sample received a pneumococcal vaccination.
