For a binomial distribution with p = 1/2 and σ = 3,the mean is µ = 18.

Question

For a binomial distribution with p = 1/2 and σ = 3,the mean is µ = 18.​

Quizplus · Accepted Answer

In a binomial distribution, the mean is given by μ = np, where n is the number of trials and p is the probability of success. We are given that p = 1/2 and μ = 18. Therefore, 18 = n(1/2), which implies n = 36.

The standard deviation of a binomial distribution is given by σ = sqrt(np(1-p)). We are given σ = 3, so 3 = sqrt(36(1/2)(1-1/2)), which is true. Therefore, the given conditions are consistent with a binomial distribution with p = 1/2 and σ = 3, and the mean is indeed μ = 18.

For a Binomial Distribution with P = 1/2 and σ