In this article, we will learn How to use the BINOM.DIST function in Excel.
What is binomial probability distribution and binomial cumulative distribution?
The Binomial Distribution is a statistical measure that is mostly used to find the probability of a specific number of successes occurring from a specific number of independent trials. For example finding the probability of winning an election of a candidate from a sample of votes. binomial distribution gives us an expected probability of the event happening. For instance, there are two outcomes of an event, either success expressed as p, or failure expressed 1-p. Probability p can take value in interval [0, 1]. Now, suppose that we perform n independent repetitions of the experiment and we observe k successes. Now we want to find the probability of the number of independent trials (x) that are to be done. The mathematical formula to find the expected value or binomial probability mass distribution of the event happening in x independent trials.
This formula is only applicable if the probability remains the same for the success and failure and You can only afford two outcomes called success and failure. You can calculate the mean for the distribution using the formula mean = np and variance = np(1-p) and standard deviation can be calculated taking the square root of the variance. You can avoid using the Expected value formula in Excel using the BINOM.DIST function. Let's learn about the BINOM.DIST function.
BINOM.DIST Function in Excel
BINOM.DIST is a statistical function which returns the expected value or the probability of success in a given number of trials having number of success in trial and probability of the succes in a trial.
BINOM.DIST Function syntax:
|=BINOM.DIST(number_s, trials, probability_s, cumulative)|
Number_s : The number of successes in trials.
Trials : The number of independent trials.
Probability_s : The probability of success on each trial.
Cumulative : logical value that determines the form of the function. If cumulative is TRUE, then BINOM.DIST returns the cumulative distribution function, which is the probability that there are at most number_s successes; if FALSE, it returns the probability mass function, which is the probability that there are exact number_s successes.
All of these might be confusing to understand. Let's understand how to use the function using an example. Here we have a situation where we have 2 red balls and 3 white balls in a bag. We started an event where we take out a ball from the bag and note its color and put the ball back in the bag. We did the task 10 times and now we want to know the probability of a red ball occurring each time in the next exact 4 turns. So for the BINOM.DIST function to use we have a number of trials, number of successes. To get the exact number of counts in 4 turns we will flag the function to FALSE. But we still want to find the probability of getting a red ball for a turn. For that we use the basic formula of probability.
Use the formula:
|= number of red balls / total number of balls|
Which will interpreted as = B2 / B1
As you see, the probability of a red ball comes out to be 0.40. Now we will use the BINOM.DIST function.
Use the formula:
As you can see the binomial cumulative distribution for the red ball exactly 4 times comes out to be 0.25 which is 1/4. Now we want to get the probability mass distribution for the same parameters for at most 4 times.
Use the formula :
As you can see, the probability mass distribution comes out to be 0.63. You can use the function for any of the probability or cumulative functions. Use the BINOM.INV function to calculate the z value for the binomial distribution.
Here are all the observational notes using the BINOM.DIST function in Excel
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