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Show the calculation to find the μ and σ of a binomial variable whose probability of success if 0.3 with a total number of attempts of 20.

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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