Binomial Distributions
The Variance
The Problem
Let X be a random variable following a Binomial distribution. All Binomial distributions have two parameters: number of trials and success probability. For X, n = 14 and p = 0.44. An example of where such a distribution may arise is the following:
You have a bag of candy made by Statistics, Inc. The company makes only two flavors: sour apple and anchovie. In its processing plant, 44% of the candy made is sour apple. Your bag holds 14 pieces. Define the random variable X as the number of sour apple pieces of candy in your bag.
For those who like pictures, here is a graphic of the probability mass function. Note that the distribution is slightly skewed right:
With this information, calculate the variance of the random variable, σ² or V[X].
Your Answer
In the box below, please enter the variance of the random variable described above, then click on the “Check your answer!” button. Please round your answer to the ten-thousandths place.
![[Correct!]](images/correct.png "You are correct. Well done!")
You got the correct answer of ![[Incorrect!]](images/incorrect.png "You are not correct.")
Unfortunately, your answer was not correct. Either try again or click on “Show Solution” below to see how to obtain the correct answer.
Assistance
Show Formula
Show Solution
Show the R Code
Show the Excel Code