Best solutions to - "What are the mean and standard deviation of..."

namenerk

Answered question

2022-01-18

What are the mean and standard deviation of a binomial probability distribution with n=144 and

p = \frac{11}{13}

usaho4w

Beginner2022-01-18Added 39 answers

Explanation:
The mean of a binomial distribution is simply:

μ = n p

Which in our case is

μ = 144 \cdot \frac{11}{13} = \frac{1584}{13} \tilde{=} 121.8

The standard deviation of the binomial distribution is given by:

σ = \sqrt{n p (1 - p)}

Which in our case is:

σ = \sqrt{144 \cdot \frac{11}{13} \cdot (\frac{2}{13})} = \frac{12}{13} \sqrt{22} \tilde{=} 4.330

Maria Lopez

Beginner2022-01-19Added 32 answers

μ = n \cdot p

= 144 \cdot \frac{11}{13}

=121.8
On the other hand, the variance is computed using the following formula:

σ^{2} = n p (1 - p)

. Therefore, the calculation goes like:

σ^{2} = n p (1 - p)

= 144 \cdot \frac{11}{13} (1 - \frac{11}{13})

=18.7

σ = \sqrt{σ^{2}} = \sqrt{18.7} = 4.33

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