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Find the standard deviation, σ, for the binomial distribution which has the stated values of n and p. Round your answer to the nearest hundredth. n = 38; p = 2/5 Group of answer choices σ = 13.55 σ = 14.40 σ = 7.87 σ = 10.28

Respuesta :

Answer:

[tex] X \sim Binom (n=38, p=2/5)[/tex]

By properties the mean is given by:

[tex]\mu = np =38 *\frac{2}{5}= 15.2[/tex]

And the standard deviation would be:

[tex] \sigma = \sqrt{np(1-p)}= \sqrt{38* \frac{2}{5}* (1-\frac{2}{5})}= 3.02[/tex]

Step-by-step explanation:

For this case we know that the random variable follows a binomial distribution given by:

[tex] X \sim Binom (n=38, p=2/5)[/tex]

By properties the mean is given by:

[tex]\mu = np =38 *\frac{2}{5}= 15.2[/tex]

And the standard deviation would be:

[tex] \sigma = \sqrt{np(1-p)}= \sqrt{38* \frac{2}{5}* (1-\frac{2}{5})}= 3.02[/tex]

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