Excel Binomial Distribution

0:00 Excel binomial distribution Intro
0:56 Binomial probability distribution
1:08 BINOM.DIST function
2:25 Graph binomial probability distribution
3:11 Changing parameters
3:32 Computing binomial distribution probabilities
4:07 Binomial probability distribution
4:15 Binomial cumulative distribution
5:15 Rewriting binomial probabilities for computation

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In this video, we will explain how you can construct a binomial distribution given a certain number of trials and the probability of success. A binomial distribution is used when you want to model a number of successes in a series of independent experiments. There are two parameters in a binomial distribution, n which represents the number of trials, and p which is the probability of success.

We start by constructing the binomial probability distribution function. This function defines all the potential values and corresponding likelihoods that a random variable can take on.

In the second step, we compute the probability corresponding to each potential outcome. To do this, we select a cell and type equals binom.dist of. First, we need to insert the number of successes we want to compute the probability of. Then we need to insert the parameters of the distribution, first the number of trials.

Next, we need the probability of success, and which we fix again using F4. Finally, we need to tell Excel which kind of distribution we want, in our case we are looking for the probability distribution function and not the cumulative distribution function. So, the final argument of our function is FALSE.

Let’s visualize this with a graph, we select the data, navigate to Insert and click on Scatter with Smooth Lines and Markers.

Before concluding this tutorial, we will show you how to compute some different kinds of probabilities. The probabilities we want to compute are listed below. We will compute the probability of exactly 10 successes, the probability of 10 successes or less than 10, the probability of less than 10 successes not including 10, the probability of more than 10 successes not including 10, and the probability of more than 10 successes including 10, and the probability that the number of successes is between 10 and 16 excluding 10 and including 16.

The first one, the probability of exactly 10 successes is already computed in the probability distribution function table.

The second probability of having 10 or fewer successes can be computed using the cumulative distribution function. This function defines the probability that a random variable takes on a value less than or equal to each potential value of the variable. We have copy-pasted our first table for the probability distribution function but changed the last argument in our BINOM.DIST function to TRUE. So, the second probability in our table is defined in the cumulative distribution table.

For the third probability, we remark that the probability of having successes strictly smaller than 10 is the same as having the number of successes equal to 9 or less.

The fifth probability is the same as 1 minus the number of successes strictly smaller than 9 and this is the same as 1 minus the number of successes smaller than or equal to 8.

Finally, to compute the probability that our number of successes is between 10 and 16 excluding 10 and including 16, we again try to rewrite this in an easier way. We remark that this is the same as computing the probability that the number of successes is smaller than or equal to 16 minus the probability that the number of successes is smaller than or equal to 10.

This concludes our tutorial on the Binomial Distribution in Excel. I'm inspired by content creators as Leila Gharani and Teacher's Tech.

#Excel #Tutorials #Statistics

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