How to find the mean: probability distribution or binomial distribution
Finding the mean of a probability distribution is easy in probability and statistics. This how to will guide you through a few simple steps necessary to find the mean. You’ll often find these types of questions in textbook chapters on binomial probability distribution.
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 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 this article on constructing 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!
Related posts:
- How to Get The Mean and Standard Deviation For a Binomial Probability Distribution With a TI 83 Calculator
- Standard deviation: binomial distribution
- How to Solve a Binomial Distribution Problem Using the Binomial Formula
- How to use the BinomialCdf function on the TI-89 to find Binomial Probability.
- How to Work a Binomial Distribution Formula
How to Do Everything Statistics » Standard deviation: binomial distribution said:
Aug 26, 09 at 12:52 pm[...] Step 1: Find the mean. If you don’t know how, see this article on how to find the mean using a probability distribution. [...]
Lisa barcomb said:
Sep 20, 09 at 3:57 amWhen 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.
Stephanie said:
Sep 20, 09 at 4:32 amI’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.
Lisa Barcomb said:
Sep 20, 09 at 5:07 amYeah 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.
Stephanie said:
Sep 20, 09 at 5:35 amYou 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!
Jennifer Thomas said:
Sep 20, 09 at 11:26 amI believe Step 4 should read:
0+.02+.04+.03 = .09
Donna Allen said:
Sep 26, 09 at 7:41 amI 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.
Vanessa DuBarry said:
Dec 10, 09 at 5:54 pmYes 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 :)
Tammy Sutton said:
Dec 12, 09 at 11:55 ammy problem is that with all of those words and the answer seems so simple.
Kristen said:
Sep 21, 11 at 5:23 pmI 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
Stephanie said:
Sep 27, 11 at 4:50 pmHi, Kristen,
Can you post your question on the discussion board? Unfortunately, I don’t have the time to answer math questions here.
Thanks,
Stephanie