Binomial Distributions

The Expected Value

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 = 24 and p = 0.56. 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, 56% of the candy made is sour apple. Your bag holds 24 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 left:

0.05 0.10 0.15 0.20 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

With this information, calculate the distribution mean, μ or E[X].

Your Answer

In the box below, please enter the mean of the distribution given above, then click on the “Check your answer!” button. Please round your answer to the ten-thousandths place.

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