Respuesta :
Using the binomial distribution, it is found that there is a 0.3222 = 32.22% probability that at least 3 Canadian are on CERB in the sample.
What is the binomial distribution formula?
The formula is:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are:
- x is the number of successes.
- n is the number of trials.
- p is the probability of a success on a single trial.
The values of the parameters are:
n = 10, p = 0.2.
The probability that at least 3 Canadian are on CERB in the sample is:
[tex]P(X \geq 3) = 1 - P(X < 3)[/tex]
In which:
P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2).
Then:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{10,0}.(0.2)^{0}.(0.8)^{10} = 0.1074[/tex]
[tex]P(X = 1) = C_{10,1}.(0.2)^{1}.(0.8)^{9} = 0.2684[/tex]
[tex]P(X = 2) = C_{10,2}.(0.2)^{2}.(0.8)^{8} = 0.3020[/tex]
Then:
P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2) = 0.1074 + 0.2684 + 0.3020 = 0.6778.
[tex]P(X \geq 3) = 1 - P(X < 3) = 1 - 0.6778 = 0.3222[/tex]
0.3222 = 32.22% probability that at least 3 Canadian are on CERB in the sample.
More can be learned about the binomial distribution at https://brainly.com/question/24863377
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