In this video, gain the skills required for using the binomial distribution.
- [Instructor] So many business questions can be answered yes or no, true or false. For example, a customer either will or will not sign up for your mailing list. In this movie, I will show you how to calculate the probabilities for outcomes described by the binomial distribution, which handles this type of yes or no case. My sample file is the Binomial Distribution, and you can find it in the Chapter Four folder of your Exercise Files collection. In this scenario, let's assume that you are asking customers to sign up for your mailing list.
You're doing them 20 at a time, and you've discovered over time that you have about a 22% success rate. So a 22% success, if you ask 20 people, you should, on average, get about 4.4 signups. To calculate a binomial probability, you need to know four things, and that is the Probability of Success, that's in B1, that's 22%, the Number of Trials, or the number of times you attempt the task, and that's in cell B2. In this case, it's 20. You need to know the number of potential successes, and those are in Column A under the Successes Column in my table.
So how many times would you expect to get zero? How many times would you expect to get one, and so on, just based on random chance? And finally, you need to know whether you're looking for the probability of a specific number of successes occurring or less. And we'll look at both elements when we create our formulas. We'll create our formulas in Column B under Percentage of Outcomes in my Excel table. So I'll click in cell B5, and I want to calculate the probability of getting zero successes, that's the value in cell A5.
So I'll type in the equal sign, and I will use the BINOM.DIST function. The Number of Successes is in cell A5. Now, I'll type a comma. I'll leave that cell reference relative so it can change as the formula's copied down. The Number of Trials is cell B2, so I'll type B2 and then F4 to make it an absolute reference, then a comma. The Probability of Success is in cell B1, so I'll type B1 followed by F4, so the cell reference doesn't change, then a comma, then whether I want to make it cumulative or whether I want to look at the probability mass function, which is the possibility of a specific value occurring.
We'll do the probability mass function first, so I'll use the data or key to highlight false, and press Tab. Those are all my arguments, so I will type a right parenthesis to close, Enter, and I get the values. So Percentage of Outcomes will be zero successes about .7% of the time. Now, I can copy the formula down to the rest of my table rows, so I'll click the AutoCorrect Options button, and I will select Overwrite all cells in this column with this formula.
So there, you see. And as you can see, the probability of getting a specific number of successes goes up as I go to four, and then going down, you see that it's less probable to get fives, still less for six, and so on, where it's very unlikely to get exactly 11 or higher. And this makes sense. The probability of success is 22%, and if I multiply that by the number of trials, on average, we should expect about 4.4 people to sign up.
Now, let's take a look at the cumulative probability distribution, so in other words, if we want to get four or less, five or less, and so on. In cell B5, I'll double-click, and I will change the FALSE argument for probability mass function to the cumulative probability distribution or TRUE, and press Enter. And you see that my table updates. So now, we see that there's less than 1% chance of getting zero signups, 4.6% of getting one or less, 15% of getting two or less, and then at four, it's 54.2%, roughly, of getting four or less, five, six, seven, and so on.
So how can you use this data? Well, if you have particular individuals who are better at getting customers to sign up for your mailing list, then they will tend to produce more than 4.4 signatures on average. And you can see how likely it is that they would generate a specific number of signups. If someone is consistently getting ten or higher signups, then you might check the data and make sure that the customer has actually intended to sign up.
- Distinguish between the mean, median, and mode.
- Describe the relationship between variance and standard deviation.
- Identify a nondirectional hypothesis.
- Point out the difference between COVARIANCE.P and COVARIANCE.S.
- Explain correlation.
- Analyze Bayes’ rule.