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Title screen: How to use Poisson.dist. Copyright ©2017 McGraw-Hill Education. All rights reserved.
Narrator: "This video will demonstrate how to apply the Poisson distribution using the Excel formula POISSON. DIST. The Poisson distribution, like the binomial and hypergeometric probability distributions, has only two outcomes—success and failure. In this example, a loan officer at a bank approved 40 loans last month. Based on many years of experience, the default rate—that is, the rate at which people will not be able to repay their installment loans—is . 025, or 2. 5%. We are seeking to answer two questions—the probability that three loans will default, and the probability that three or more loans will default. This is the dialogue box for the POISSON. DIST formula in Excel."
A screenshot of the Function Arguments dialog box, which contains three text fields: X, Mean, and Cumulative. Text is overlaid in each field: X, number of successes; Mean, Expected number of succeses; Cumulative, true or false.
Narrator: "Note that we only need three pieces of information. First is 'X.' What is it we are seeking the probability of? In the first question, we're seeking the probability that exactly three loans will default—i. e. P(x)=3. The mean is the expected number of loans that will default in that interval. Since we know . 025 is the default rate, and the loan officer made 40 loans, then . 025 times 40 equals one loan. The cumulative value can either be true or false. True means we are seeking the probability up to and including some value of 'X.'"
Text: True: P left parenthesis X right parenthesis less than or equal to some value.
Narrator: "False means we are seeking the probability of 'X' equals some value. For the first question, we will use false. Let's open the dialogue box, enter our information, and solve the first question. =POISSON. DIST( F(x) to open the dialogue box."
The formula is entered into cell G7 and the F x button, left of the formula bar above the sheet, is clicked to open the Function Arguments dialog box.
Narrator: "Here, we are looking for the probability that three loans will default. And the mean, which we can calculate in the cell, is . 025 times 40 loans given in one month. Cumulative will be false, because we want to know the exact probability for three loans defaulting."
The full formula in cell G7: equals Poisson dot Dist left parenthesis three comma 0.025 times 40 comma false right parenthesis.
Narrator: "And that probability is just over 6%. The next question asks, 'What is the probability of three or greater loans defaulting?' So we are seeking 'greater than or equal to.'"
Text: P left parenthesis x right parenthesis greater than or equal to three.
Narrator: "Cumulative will tell us 'less than or equal to.' We can find the probability of two or fewer loans in default and then subtract that from 100%, which will tell us the probability of three or greater being in default."
Text: One minus P left parenthesis x right parenthesis less than or equal to two is the same as P left parenthesis x right parenthesis greater than or equal to three.
Narrator: "Let's compute it directly in the cell. =1-POISSON. DIST. The 'X' we care about here is 2, because remember we're going to do two or fewer and subtract it from 1 to get the 3 or greater. The mean is still . 025 x 40. So, this is . 025 of the loans in a month. And then true."
The formula in cell G8: equals one minus poisson dot dist left parenthesis 2 comma point 025 times 40 comma true right parenthesis.
Narrator: "And the probability is 8% that at least three loans will default. This video has demonstrated how to use the POISSON. DIST formula to apply the Poisson probability distribution."
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Described transcript ©2023 McGraw Hill. All rights reserved. No reproduction or further distribution permitted without the prior written consent of McGraw Hill.
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