Ben Shaver

2022-01-18

What are the mean and standard deviation of a binomial probability distribution with n=150 and $p=\frac{7}{9}$?

temzej9

Expert

mean =np

Explanation:
$mean=150×\frac{7}{9}=\frac{350}{3}\approx 116.7$

accimaroyalde

Expert

Solution:
The mean of the binomial distribution is interpreted as the mean number of successes for the distribution. To find the mean, use the formula
$\mu =n\cdot p$
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
$\mu =150\cdot \frac{7}{9}$
Multiplying the expression we have
$\mu =115.5$
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
$\sigma =\sqrt{n\cdot p\cdot \left(1-p\right)}$
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
$\sigma =\sqrt{150\cdot \frac{7}{9}\cdot \left(1-\frac{7}{9}\right)}$
Evaluating the expression on the right, we have
$\sigma =\sqrt{26.565}$
$\sigma =5.09$

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