For a binomial distribution with p = 1/4 and a mean of m = 12,the standard deviation is s = 9.

Question

For a binomial distribution with p = 1/4 and a mean of m = 12,the standard deviation is s = 9.​

Quizplus · Accepted Answer

This statement is false. If the mean is 12 and the probability of success is 1/4, we can use the formula for the mean of a binomial distribution, which is np, where n is the number of trials. So, we have:

12 = n * (1/4)
n = 48

Now, we can use the formula for the standard deviation of a binomial distribution, which is sqrt(np(1-p)). Plugging in the values, we get:

s = sqrt(48*(1/4)*(3/4)) = 3sqrt(3)

So the standard deviation is not 9, but approximately 5.196.

For a Binomial Distribution with P = 1/4 and a Mean