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

What is the mean of a binomial random variable with n = 18 and p = 0.4?
Answer: 7.2
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

What is the standard deviation of a binomial distribution with n = 18 and p = 0.4? Round your answer to two decimal places.
Answer: 2.08
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

What is the variance of a binomial distribution with n = 25 and p = 0.35? Round your answer to two decimal places.
Answer: 5.69
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.

A binomial distribution with p = 0.14 has a mean of 18.2. What is n?
Answer: 130
The mean of a random variable X is denoted
For a binomial distribution, the mean has a special formula:
In this case, p = 0.14 and
is 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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