Respuesta :
Using the binomial distribution, we have that:
- The mean is of [tex]\mu = 6[/tex].
- The standard deviation is of [tex]\sigma = 2.05[/tex].
What is the binomial probability distribution?
It is the probability of exactly x successes on n repeated trials, with p probability of a success on each trial.
The expected value of the binomial distribution is:
[tex]\mu = np[/tex]
The standard deviation of the binomial distribution is:
[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]
For this problem, the parameters are:
n = 20, p = 0.3.
Hence:
- [tex]\mu = np = 20 \times 0.3 = 6[/tex]
- [tex]\sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{20 \times 0.3 \times 0.7} = 2.05[/tex]
More can be learned about the binomial distribution at https://brainly.com/question/24863377
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