Alfred Martin

2022-01-19

What are the mean and standard deviation of a binomial probability distribution with n=10 and $p=\frac{4}{5}$ ?

lovagwb

Beginner2022-01-19Added 50 answers

Explanation:

$Mean=np=10\times \frac{4}{5}=8$

$SD=\sqrt{npq}$

$q=1-p=1-\frac{4}{5}=\frac{1}{5}$

$SD=\sqrt{10\times \frac{4}{5}\times \frac{1}{5}}=1.265$

Nadine Salcido

Beginner2022-01-20Added 34 answers

The mean of the binomial distribution is interpreted as the mean number of successes for the distribution. To find the mean, use the formula

where n is the number of trials and p is the probability of success on a single trial. Substituting values for this problem, we have

Multiplying the expression we have

The standard deviation of the binomial distribution is interpreted as the standard deviation of the number of successes for the distribution. To find the standard deviation, use the formula

where n is the umber of trials and p is the probability of success on a single trial. Substituting values fo this problem, we have

Evaluating the expression on the right, we have

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