Respuesta :
Using the binomial distribution, it is found that this is not a good strategy, as the probability that enough workers show up is below 90%.
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.
For this problem, the values of the parameters are given by:
n = 13, p = 0.95.
The probability that at least 12 workers show up is:
P(X >= 12) = P(X = 12) + P(X = 13)
Applying the binomial distribution formula, we have that:
- P(X = 12) = 13 x (0.95)^12 x 0.05 = 0.3512.
- P(X = 13) = (0.95)^13 = 0.5133.
Then, the probability that enough workers show up is given by:
P(X >= 12) = P(X = 12) + P(X = 13) = 0.3512 + 0.5133 = 0.8645 = 86.45%.
This is not a good strategy, as the probability that enough workers show up is below 90%.
More can be learned about the binomial distribution at https://brainly.com/question/24863377
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