1. ThePoisson probability distributionis useful when determining the likelihood of achievingrnumber of successes in a specified interval of time or physical space.

It is named for a French mathematician and is a discrete probability distribution, since it applies only to counting number values of the random variable being investigated.

Agree or disagree?

Agree

Disagree

QUESTION 2

In order to apply the Poisson discrete probability distribution to any given context,two(2) assumptions must be met: (1) the probability of an event occurring is the same for any two intervals of equal length, and (2) the occurrence or non-occurrenceof the event is independent of it occurring in any other interval of time or space.

Agree or disagree?

Agree

Disagree

QUESTION 3

Which,if any, of the following contexts could represent applicationsof the Poisson discrete probability distribution?

Check all appropriate contexts.

	a.	Determining the likelihood that seven stocks in a portfolio of twenty-five stocksmanaged by Empire Equities will close higher on a given day when,from past experience,20% have closed higherrecently.
	b.	Determining the likelihood that between twelve and sixteen cars arrive at the drive-up window at Bernie's Burgers during the half hour starting at 4:30 pm when twenty are expectedon average.
	c.	Determining the likelihood that a slice ofMega Mart house brand cinnamon raisinbread containsexactly ten raisins when each slice should have on averageeight.
	d.	Determining the likelihood a square mile of downtown real estate contains no more than two Corner Cafecoffee shops when the company reports on average three shops per square mile.
	e.	Determining the likelihood that the staff of Dinah's Diner prepares one-dozen take-out orders during the 9o'clockhour on any weekday when on average they routinely prepareone-half dozen during that time period.

QUESTION 4

As a review, which,if any, of the following contexts could represent applicationsof the binomial discrete probability distribution?

Check all appropriate contexts.

	a.	Determining the likelihood that seven stocks in a portfolio of twenty-five stocksmanaged by Empire Equities will close higher on a given day when,from past experience,20% have closed higherrecently.
	b.	Determining the likelihood that a slice ofMega Mart house brand cinnamon raisinbread containsexactly ten raisins when each slice should have on averageeight.
	c.	Determining the likelihood a square mile of downtown real estate contains no more than two Corner Cafecoffee shops when the company reports on average three shops per square mile.
	d.	Determining the likelihood that the staff of Dinah's Diner prepares one-dozen take-out orders during the 9o'clockhour on any weekday when on average they routinely prepareone-half dozen during that time period.
	e.	Determining the likelihood that between twelve and sixteen cars arrive at the drive-up window at Bernie's Burgers during the half hour starting at 4:30 pm when twenty are expectedon average.

QUESTION 5

Unfortunately,computing the likelihood of a random variable that adheres to a Poisson discrete probability distribution is not readily completed without using technology,because the formula involves both an irrational number constant,e, exponentiation, and factorials, a special product of counting numbers.

Here's the formula, for your information for determining probabilities involving a Poisson distribution:

, whereis the expected value of the random variable over the interval.

NOTES:Thenon-terminating,non-repeatingnumberehas the approximatevalue,2.718281828459045...It is a growth constant,first identified in order to provide compound interestcontinuously.

The formula can be utilized with ascientificcalculator.However,spreadsheetfunctions can much more readily provide these calculations: =POISSON.DIST(

Agree or disagree?

Agree

Disagree

QUESTION 6

In order to test the spreadsheet function,consider the following context:

The banana walnut muffins at CornerCafecontain on average the equivalent of three chopped walnuts. What is the chance a randomly selected muffin is especially nutty and contains the equivalentof five chopped walnuts?

Using a scientific calculator, or using a spreadsheet simply as a calculator, the answer is approximately 0.100819.

Using the spreadsheetfunction, ...

=POISSON.DIST(5,3,false)

the same answeris generated. NOTE: the choice FALSE is selected for a discrete probability distribution such as the Poisson because this question requires an exact not cumulative answer. Had the question read, what was the chance that no more than five chopped walnuts were in the muffin, the responsewould have been TRUE.

You have tried the function and generated the correct answer,AGREED?

Agree

Disagree

QUESTION 7

Now try the cumulative example:

Whatis the chance a randomly selectedbanana walnut muffin contained no more than five choppedwalnuts?

Repeat the function, using TRUE rather than FALSE.

You are doing the work of six formulas. Imagine manually calculating with a scientific calculator the chance of exactly 0,1,2,3,4, and 5 chopped walnuts. That's what you are doing.

Anyway, report your answer rounded to the nearest wholepercentage: #% or ##%

QUESTION 8

Try this example.

What is the chance that a banana walnut muffin at Corner Cafecontains at least two but no more than four chopped walnuts if the average is three?

You can simply perform the function three times for the values that work: two, three and four. Then, add them up. You would use the FALSE response when prompted.

=POISSON.DIST(2,3,false)+POISSON.DIST(3,3,false)+POISSON.DIST(4,3,false)

You can more efficientlyapply the spreadsheet function twice, subtracting the find the difference with the TRUE response this time, but be careful. We want to include two in the final answer, not exclude it.

=POISSON.DIST(4,3,true)-POISSON.DIST(2,3,true)...doesNOTprovide thesame answer!! We end up throwing out the chance of two chopped walnuts in that subtraction. No, thanks!

Let's edit that line slightly. What do you think? We want to include 2, 3, and 4, so what should change?

What number should replace the hash tag symbol here?

=POISSON.DIST(4,3,true)-POISSON.DIST(#,3,true)

QUESTION 9

Now, report the answer to this question, rounded to the nearest wholpercentage: #% or ##%

What is the chance that a banana walnut muffin at CornerCafecontains at least two but no more than four chopped walnuts if the average is three?

=POISSON.DIST(2,3,false)+POISSON.DIST(3,3,false)+POISSON.DIST(4,3,false)

=POISSON.DIST(4,3,true)-POISSON.DIST(#,3,true)

QUESTION 10

Now consider this context:

Based on new pandemic-generated public health guidelines,Corner Cafecoffee shops must be able to provide adequate safe wait line space in their stores in order to reopen. The busiest stores expect on average six customerswaiting to order at any time during the morning rush. The management is deciding how much floor space to allot for these queues. They wonder what is the chance at least eight customers will be waiting and need to be accommodated at any given time?

This question asks the chance of 8, 9, 10, or more waiting. Unfortunately, spreadsheet functions are routinely oriented for cumulative cases (TRUE prompt) from the valueof interestdownto zero, not up. However, we can employ complementary probability strategies, by subtracting what we don't want form the whole or 100%.

Try this option. If we seek the chance of at least eight, we don;t want seven or fewer.

=1-POISSON.DIST(7,6,true)

Report the answerrounded to the nearest whole percentage.

COMMENT: If the answer exceeds 25%, the management will wantto assignmore floor space than previously planned for the queue and safe social distancing.