Figuring Out the Mean, Variance, and Standard Deviation of a Binomial Random Variable - dummies

# Figuring Out the Mean, Variance, and Standard Deviation of a Binomial Random Variable

Solving statistics problems can involve finding probabilities, mean, and standard deviation for a specific random variable, in this case the binomial. Solve the following problems about the mean, standard deviation, and variance of binomial random variables.

## Sample questions

1. What is the mean of a binomial random variable with n = 18 and p = 0.4?

The mean of a binomial random variable X is represented by the symbol

A binomial distribution has a special formula for the mean, which is

Here, n = 18 and p = 0.4, so

2. What is the standard deviation of a binomial distribution with n = 18 and p = 0.4? Round your answer to two decimal places.

The standard deviation of X is represented by

and represents the square root of the variance. If X has a binomial distribution, the formula for the standard deviation is

where n is the number of trials and p is the probability of success on each trial. For this situation, n = 18 and p = 0.4, so

3. What is the variance of a binomial distribution with n = 25 and p = 0.35? Round your answer to two decimal places.

The variance is represented by

and represents the typical squared distance from the mean for all values of X.

For a binomial distribution, the variance has its own formula:

In this case, n = 25 and p = 0.35, so

Rounded to two decimal places, the answer is 5.69.

4. A binomial distribution with p = 0.14 has a mean of 18.2. What is n?