Statistics How To

Find the mean of the probability distribution or binomial distribution

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How to find the mean of the probability distribution : Overview

How to find the mean of the probability distribution

A normal distribution curve is one kind of probability distribution.


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).)
    probability distribution toms
  • 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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13 thoughts on “Find the mean of the probability distribution or binomial distribution

  1. Lisa barcomb

    When you are finding the mean it is pretty easy but when you get into the mean for probability distribution it tends to be alittle tricky. I am really having a hard time with Chapter 3. I think what it is that there are so many words its like a word problem and it tends to confuse me. I am not the best person in doing math but I do like it because its a challenge to me and a building block of knowledge. I am working real hard on getting this information. If anyone has any ideas please let me know your secrets.

  2. Stephanie

    I’m glad you are enjoying the challenge. I’m not sure I have any “secrets” :) I was a poor math student all the way through my undergrad (my major was health science, not math). Math finally clicked for me in my first year of grad school, and I wish I knew what clicked so I could share it! Just keep on working the problems and it will click eventually.

  3. Lisa Barcomb

    Yeah because at some point I really feel like I am stupid and this is a foreign language to me so I am working really hard to figure this out so I can come out knowing somethings about this particular subject. I just wish it would click with me. Maybe its because I am over 40 and your brain can only do so much but I would really like to show myself that I can do this.

  4. Stephanie

    You aren’t stupid :) I started my master’s degree at 35 and it was very, very hard (compared to my undergrad, when learning came easily). There were a couple of occasions I threw my textbooks in the trash, convinced I couldn’t do it (the time I took linear algebra and statistics with calculus at the same time–big mistake,lol). Stick with it and eventually it WILL click–trust me, I’ve been there!

  5. Donna Allen

    I agree with Lisa. To me, looking at the word problem itself is a bit overwhelming. After reading your explanation and practicing the problems, it is starting to click how to pick out the numbers and fit them into the equations. I have also had some very frustrated times since starting this class. Math has never been my best subject. I completely understand feeling overwhelmed.

  6. Vanessa DuBarry

    Yes math can be overwhelming,I am alwayas thinking negative about math from the start and i convince myself that i cant do it that its too hard, but this course has taught me to take one step at a time,to think positive and to never give up! esp with blogs like this one that makes it a whole lot easier :)

  7. Kristen

    I am helping my son with his homework and I want to make sure that my assumptions are correct before I help him with this question. I have modified the question a bit from his homework to simplify.

    I think his question is similar to your example above:
    If you have a spinner with 4 zones and you win a certain number of coins in each of the zones (number of coins listed under zone below). The probably of landing in each of the zones is unequal (given below).
    The question is:
    What is the mean number of coins you expect to win in a single spin in the game?

    Zone Probability %
    0 17
    1 40
    3 10
    25 2

    so
    0*.17=0
    1*.40=.4
    3*.10=.3
    25*.02=.5
    0+.4+.3+.5=1.2 coins is the mean you can expect in a single spin

  8. Stephanie

    Hi, Kristen,
    Can you post your question on the discussion board? Unfortunately, I don’t have the time to answer math questions here.
    Thanks,
    Stephanie

  9. Steve

    For a binomial distribution, it’s much faster to multiply the number of trials (n) by the probability of success (p). So, the mean for a binomial distribution is np. I couldn’t find that method on your site. So for example, if a basketball player has a 90% chance of making any given free throw attempt and we assume all the binomial conditions are met, then during a practice session where the player makes 30 attempts at a free throw, the average number of shots actually made successfully would be (30)(.9)=27.

  10. Andale

    Steve,
    Thanks for your note. Step 3 does multiply p*n (technically), when you multiply the probability by the rotten tomatoes. However, this how to is for the mean (so you would be looking at the average several basketball players with several attempts each at free throws).
    Stephanie