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

What is the mean of a binomial random variable with

*n*= 18 and*p*= 0.4?**Answer:**7.2The mean of a binomial random variable

*X*is represented by the symbolA binomial distribution has a special formula for the mean, which is

Here,

*n*= 18 and*p*= 0.4, soWhat is the standard deviation of a binomial distribution with

*n*= 18 and*p*= 0.4? Round your answer to two decimal places.**Answer:**2.08The standard deviation of

*X*is represented byand represents the square root of the variance. If

*X*has a binomial distribution, the formula for the standard deviation iswhere

*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, soWhat is the variance of a binomial distribution with

*n*= 25 and*p*= 0.35? Round your answer to two decimal places.**Answer:**5.69The 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, soRounded to two decimal places, the answer is 5.69.

A binomial distribution with

*p*= 0.14 has a mean of 18.2. What is*n?***Answer:**130The mean of a random variable

*X*is denotedFor a binomial distribution, the mean has a special formula:

In this case,

*p*= 0.14 andis 18.2, so you need to find

*n.*Plug the known values into the formula for the mean, so 18.2 =*n*(0.14), and then divide both sides by 0.14 to get*n*= 18.2/0.14 = 130.

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