"What are the mean and standard deviation of..." was answered by students like you

Quentin Johnson

Answered question

2022-01-19

What are the mean and standard deviation of a binomial probability distribution with n=12 and

p = \frac{3}{5}

reinosodairyshm

Beginner2022-01-19Added 36 answers

Explanation:
Mean of a binomial probability distribution is given by np and standard deviation is given by

\sqrt{n} p q

, where q=1-p.
In the given example,

n p = 12 \cdot \frac{3}{5} = 7.2,

q = 1 - \frac{3}{5} = \frac{2}{5}, \sqrt{n} p q = \sqrt{12 \cdot \frac{3}{5} \cdot \frac{2}{5}} = \frac{1}{5} \cdot \sqrt{72} = 6 \frac{\sqrt{2}}{5} = 1.697

Hence mean is 7.2 and standard deviation is 1.697

Elois Puryear

Beginner2022-01-20Added 30 answers

The formula for the population mean is

μ = n \cdot p

, so therefore we get:

μ = n \cdot p

= 12 \cdot \frac{3}{5}

=7.2
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)

= 12 \cdot \frac{3}{5} (1 - \frac{3}{5})

=2.88
And finally, taking square root to the variance we get that the population standard deviation is:

σ = \sqrt{σ^{2}} = \sqrt{2.88} = 1.697

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