How to Work a Binomial Distribution Formula

binomial distribution 7 Comments

The binomial  formula can calculate the probability of success for binomial distributions. Often you’ll be told to “plug in” the numbers to the formula and calculate. This is easy to say, but not so easy to do–unless you are very careful with order of operations, you won’t get the right answer. If you have a Ti-83 or Ti-89, the calculator can do much of the work for you. If not, here’s how to break down the problem into simple steps so you get the answer right–every time.

binomialprobabilityformula

Step 1:: Read the question carefully.  Sample question: “80% of people who purchase pet insurance are women.  If 9 pet insurance owners are randomly selected, find the probability that exactly 6 are women.”

Step 2:: Identify ‘n’ and ‘X’ from the problem. Using our sample question, n (the number of randomly selected items) is 9,  and  X (the number you are asked to find the probability for) is 6.

Step 3: Work the first part of the formula. The first part of the formula is

n! / (n – X)!  X!

Substitute your variables:

9! / ((9 – 6)! × 6!)

Which equals 84. Set this number aside for a moment.

Step 4: Find p and q. p is the probability of success and q is the probability of failure. We are given p = 80%, or .8. So the probability of failure is 1 – .8 = .2 (20%).

Step 5: Work the second part of the formula.

pX
= .86
= .262144

Set this number aside for a moment.

Step 6: Work the third part of the formula.

q(n – X)
= .2(9-6)
= .23
= .008

Step 7: Multiply your answer from step 3, 5, and 6 together.
84  × .262144 × .008 = 0.176.

That’s it!

Related posts:

  1. How to Solve a Binomial Distribution Problem Using the Binomial Formula
  2. How to read a binomial distribution table
  3. How to Use the Binomial Distribution Calculator
  4. How to find the mean: probability distribution or binomial distribution
  5. How to determine if something is a binomial experiment
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7 Responses to “How to Work a Binomial Distribution Formula”

  1. Scott Selph said:

    Oct 05, 09 at 6:26 am

    This explains everything much simpler than the book. The step-by-step guidance is just what I needed. Thank You

  2. angie widdows said:

    Nov 03, 09 at 6:03 pm

    Things get so confusing on when to subtract from 1 or to subtract from .5000. Is there any special reasoning or logic on which one to use.

  3. crystal lydick said:

    Feb 01, 10 at 8:07 am

    I keep getting so lost on step #3 , I never get the right answer to this portion of the problem. Can someone walk me through exactly what I am suppose to do at that point??? Thank you ih advance.

  4. John said:

    Feb 01, 10 at 10:17 am

    Crystal…I get stuck on this part myself. You might have better luck asking in the forums. JP

  5. crystal lydick said:

    Feb 01, 10 at 7:17 pm

    Thanks John, This is driving me insane I cannot figure it out!! I have done terrible on the quiz. I have one more chance to take it, but I don’t know how to work 3 of the problems!! Hope you did better than I have!

  6. jamie said:

    Apr 19, 11 at 5:58 pm

    thankyou so so so much! God bless you youve helped me so much

  7. Alex said:

    May 18, 11 at 9:21 pm

    This just saved my life. I cant fail business statistics again for the 3rd time!

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