Find out the answer to "What are the mean and standard deviation of..."

Talamancoeb Answered2022-01-18

What are the mean and standard deviation of a binomial probability distribution with n=8 and

p = \frac{7}{29}

Answer & Explanation

psor32

Expert

2022-01-18Added 33 answers

m e a n = \frac{56}{29}

s \tan d a r d d e v i a t i o n = \frac{4 \sqrt{77}}{29}

Explanation:
Given Binomial Probability Distribution

m e a n = n p = 8 \cdot \frac{7}{29} = \frac{56}{29}

s \tan d a r d d e v i a t i o n = \sqrt{n p (1 - p)} = \sqrt{8 \cdot \frac{7}{29} \cdot \frac{22}{29}} = \frac{4 \sqrt{77}}{29}

Thomas White

Expert

2022-01-19Added 40 answers

μ = n \cdot p

= 8 \cdot \frac{7}{29}

=1.92
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)

= 8 \cdot \frac{7}{29} (1 - \frac{7}{29})

=1.4592
And finally, taking square root to the variance we get that the population standard deviation is:

σ = \sqrt{σ^{2}} = \sqrt{1.4592} = 1.208

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