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How to find the mean of the probability distribution : Overview
Finding the mean of a probability distribution is easy in probability and statistics — if you know how. This how to will guide you through a few simple steps necessary to find the mean of the probability distribution or binomial distribution. You’ll often find these types of questions in textbook chapters on binomial probability distribution. The binomial distribution is just a simple trial where there are two outcomes: success or failure. For example, if you are counting how many times you draw an Ace from a deck of cards, you could assign “Success” to “Drawing an Ace” and “Failure” to drawing any other card. You can find the mean of the probability distribution by creating a probability table.
How to find the mean of the probability distribution: Steps
Sample question: “A grocery store has determined that in crates of tomatoes, 95% carry no rotten tomatoes, 2% carry one rotten tomato, 2% carry two rotten tomatoes, and 1% carry three rotten tomatoes. Find the mean number of rotten tomatoes in the crates.”
- Step 1: Convert all the percentages to decimal probabilities. For example:
95% = .95
2% = .02
2% = .02
1% = .01
- Step 2: Construct a probability distribution table. (If you don’t know how to do this, see how to construct a probability distribution).)
- Step 3: Multiply the values in each column. (In other words, multiply each value of X by each probability P(X).)
Referring to our probability distribution table:
0 × .95 = 0
1 × .02 = .02
2 × .02 = .04
3 × .01 = .03
- Step 4: Add the results from step 3 together.
0 + .02 + .04 + .03 = .09 is the mean.
You’re done finding the mean for a probability distribution!
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