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There are two main characteristics of a Poisson experiment.

  1. The Poisson probability distribution gives the probability of a number of events occurring in a fixed interval of time or space if these events happen with a known average rate and independently of the time since the last event. For example, a book editor might be interested in the number of words spelled incorrectly in a particular book. It might be that, on the average, there are five words spelled incorrectly in 100 pages. The interval is the 100 pages.
  2. The Poisson distribution may be used to approximate the binomial if the probability of success is "small" (such as 0.01) and the number of trials is "large" (such as 1,000). You will verify the relationship in the homework exercises. n is the number of trials, and p is the probability of a "success."

The random variable X = the number of occurrences in the interval of interest.

The average number of loaves of bread put on a shelf in a bakery in a half-hour period is 12. Of interest is the number of loaves of bread put on the shelf in five minutes. The time interval of interest is five minutes. What is the probability that the number of loaves, selected randomly, put on the shelf in five minutes is three?

Let X = the number of loaves of bread put on the shelf in five minutes. If the average number of loaves put on the shelf in 30 minutes (half-hour) is 12, then the average number of loaves put on the shelf in five minutes is ( 5 30 ) (12) = 2 loaves of bread.

The probability question asks you to find P ( x = 3).

Try it

The average number of fish caught in an hour is eight. Of interest is the number of fish caught in 15 minutes. The time interval of interest is 15 minutes. What is the average number of fish caught in 15 minutes?

( 15 60 ) (8) = 2 fish

A bank expects to receive six bad checks per day, on average. What is the probability of the bank getting fewer than five bad checks on any given day? Of interest is the number of checks the bank receives in one day, so the time interval of interest is one day. Let X = the number of bad checks the bank receives in one day. If the bank expects to receive six bad checks per day then the average is six checks per day. Write a mathematical statement for the probability question.

P ( x <5)

Try it

An electronics store expects to have ten returns per day on average. The manager wants to know the probability of the store getting fewer than eight returns on any given day. State the probability question mathematically.

P ( x <8)

You notice that a news reporter says "uh," on average, two times per broadcast. What is the probability that the news reporter says "uh" more than two times per broadcast.

This is a Poisson problem because you are interested in knowing the number of times the news reporter says "uh" during a broadcast.

a. What is the interval of interest?

a. one broadcast

b. What is the average number of times the news reporter says "uh" during one broadcast?

b. 2

c. Let X = ____________. What values does X take on?

c. Let X = the number of times the news reporter says "uh" during one broadcast.
x = 0, 1, 2, 3, ...

d. The probability question is P (______).

d. P ( x >2)

Questions & Answers

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SHERO
Causes of economic growth
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What is elasticity of demand
pierre
What are the causes of economic growth
pierre
economic growth, establishment of industry, encourage of investor's, farm productivities, creation of institutions, construction of good road etc
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elasticity of demand can be said to be the responsiveness of demand to a change in prices
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Institution involved in money market
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Economic is the study of scarcity
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Economics is the study of a lot of things. It is split up into two areas of study, Microeconomics and Macroeconomics. Microeconomics is the study of an individual's choices in the economy and Macroeconomics is the study of the economy as a whole.
The
Economics is a science that studies human scarcity
Agnes
What is Equilibrium price?
Agnes
Equilibrium is the market clearing price. The point at which quantity demanded equals quantity supplied. The point at which the supply and demand curves intersect.
The
Equilibrium price*
The
Refers to the study of how producers use limited resources to satisfy human unlimited wants
Gatoya
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What will you do as a consumer if you are not at equilibrium?
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different levels of utilities of a person in a given set of bundles of goods
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state the law of diminishing return?
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The Law of Diminishing (Marginal) Returns simply states that at some point in time a business/operation/etc.'s increased productivity will begin to decline.
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For example, if a small pizza shop currently has 3 workers in the kitchen at any given time,and hiring 1 more worker will increase productivity, at some number of workers hired will the business see a decrease in productivity because the capital resources that the pizza shop has is not infinite.
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Five social benefits of building a hospital, in my opinion and depending on where it's built, would be 1) Increased care for neighboring residents, 2) Potential jobs for individuals, 3) May decrease the travel time residents need to endure in order to reach the nearest hospital
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4) May create work-study programs for individuals who aspire to be future Doctors, Nurses, Physicians, etc. 5) Assuming there are local pharmaceutical businesses nearby, the hospital may decide to purchase supplies local, increasing the business' sales. Thus, generating more income.
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racing to see their injured friends, family members, etc. 4) Constructing a hospital and hiring staff is very expensive 5) To use funds, private or public, to finance the construction of a hospital cannot be used to fund any other projects. (The concept of opportunity costs.)
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We use a Supply and Demand graph to illustrate at what price level will the market for a certain good or service be at equilibrium. If the price for a good or service is set too high, consumers will be less inclined to buy that product Thus, creating a surplus.
The
This surplus will eventually drive the price back down to it's equilibrium point. Similarly, if a price for a good or service is set too low, individuals would be more inclined to buy more of a certain product, creating a shortage. This shortage will cause sellers to drive the price back up to the
The
equilibrium point.
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in a comparison of the stages of meiosis to the stage of mitosis, which stages are unique to meiosis and which stages have the same event in botg meiosis and mitosis
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Source:  OpenStax, Statistics i - math1020 - red river college - version 2015 revision a - draft 2015-10-24. OpenStax CNX. Oct 24, 2015 Download for free at http://legacy.cnx.org/content/col11891/1.8
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