<< Chapter < Page Chapter >> Page >

References

“ATL Fact Sheet,” Department of Aviation at the Hartsfield-Jackson Atlanta International Airport, 2013. Available online at http://www.atlanta-airport.com/Airport/ATL/ATL_FactSheet.aspx (accessed May 15, 2013).

Center for Disease Control and Prevention. “Teen Drivers: Fact Sheet,” Injury Prevention&Control: Motor Vehicle Safety, October 2, 2012. Available online at http://www.cdc.gov/Motorvehiclesafety/Teen_Drivers/teendrivers_factsheet.html (accessed May 15, 2013).

“Children and Childrearing,” Ministry of Health, Labour, and Welfare. Available online at http://www.mhlw.go.jp/english/policy/children/children-childrearing/index.html (accessed May 15, 2013).

“Eating Disorder Statistics,” South Carolina Department of Mental Health, 2006. Available online at http://www.state.sc.us/dmh/anorexia/statistics.htm (accessed May 15, 2013).

“Giving Birth in Manila: The maternity ward at the Dr Jose Fabella Memorial Hospital in Manila, the busiest in the Philippines, where there is an average of 60 births a day,” theguardian, 2013. Available online at http://www.theguardian.com/world/gallery/2011/jun/08/philippines-health#/?picture=375471900&index=2 (accessed May 15, 2013).

“How Americans Use Text Messaging,” Pew Internet, 2013. Available online at http://pewinternet.org/Reports/2011/Cell-Phone-Texting-2011/Main-Report.aspx (accessed May 15, 2013).

Lenhart, Amanda. “Teens, Smartphones&Testing: Texting volum is up while the frequency of voice calling is down. About one in four teens say they own smartphones,” Pew Internet, 2012. Available online at http://www.pewinternet.org/~/media/Files/Reports/2012/PIP_Teens_Smartphones_and_Texting.pdf (accessed May 15, 2013).

“One born every minute: the maternity unit where mothers are THREE to a bed,” MailOnline. Available online at http://www.dailymail.co.uk/news/article-2001422/Busiest-maternity-ward-planet-averages-60-babies-day-mothers-bed.html (accessed May 15, 2013).

Vanderkam, Laura. “Stop Checking Your Email, Now.” CNNMoney, 2013. Available online at http://management.fortune.cnn.com/2012/10/08/stop-checking-your-email-now/ (accessed May 15, 2013).

“World Earthquakes: Live Earthquake News and Highlights,” World Earthquakes, 2012. http://www.world-earthquakes.com/index.php?option=ethq_prediction (accessed May 15, 2013).

Chapter review

A Poisson probability distribution of a discrete random variable gives the probability of a number of events occurring in a fixed interval of time or space, if these events happen at a known average rate and independently of the time since the last event. The Poisson distribution may be used to approximate the binomial, if the probability of success is "small" (less than or equal to 0.01) and the number of trials is "large" (greater than or equal to 25). Other rules of thumb are also suggested by different authors, but all recognize that the Poisson distribution is the limiting distribution of the binomial as n increases and p approaches zero.

The formula for computing probabilities that are from a Poisson process is:

P ( x ) = μ x e - μ x !

where P(X) is the probability of successes, μ (pronounced mu) is the expected number of successes, e is the natural logarithm approximately equal to 2.718, and X is the number of successes per unit, usually per unit of time.

Formula review

X ~ P ( μ ) means that X has a Poisson probability distribution where X = the number of occurrences in the interval of interest.

X takes on the values x = 0, 1, 2, 3, ...

The mean μ or λ is typically given.

The variance is σ 2 = μ , and the standard deviation is
σ  =  μ .

When P ( μ ) is used to approximate a binomial distribution, μ = np where n represents the number of independent trials and p represents the probability of success in a single trial.

P ( x ) = μ x e - μ x !

Use the following information to answer the next six exercises: On average, a clothing store gets 120 customers per day.

Assume the event occurs independently in any given day. Define the random variable X .

What values does X take on?

0, 1, 2, 3, 4, …

What is the probability of getting 150 customers in one day?

What is the probability of getting 35 customers in the first four hours? Assume the store is open 12 hours each day.

0.0485

What is the probability that the store will have more than 12 customers in the first hour?

What is the probability that the store will have fewer than 12 customers in the first two hours?

0.0214

Which type of distribution can the Poisson model be used to approximate? When would you do this?


Use the following information to answer the next six exercises: On average, eight teens in the U.S. die from motor vehicle injuries per day. As a result, states across the country are debating raising the driving age.

Assume the event occurs independently in any given day. In words, define the random variable X .

X = the number of U.S. teens who die from motor vehicle injuries per day.

X ~ _____(_____,_____)

What values does X take on?

0, 1, 2, 3, 4, ...

For the given values of the random variable X , fill in the corresponding probabilities.

Is it likely that there will be no teens killed from motor vehicle injuries on any given day in the U.S? Justify your answer numerically.

No

Is it likely that there will be more than 20 teens killed from motor vehicle injuries on any given day in the U.S.? Justify your answer numerically.

Questions & Answers

what is class bryophyta
Emefa Reply
how many stages do we have in glycolysis?
Damali
10 stages
Elisha
the presence of a membrane enclosed nuclosed is a characteristics of what
Addai Reply
eukaryotic cell
captain
hetreothalism in fungi
Lekhram Reply
there are 3 trimester in human pregnancy
ROHIN Reply
I don't know answer of this question can u help me
ROHIN
yes
Bisa
what is a cell
Fatima Reply
A cell is functional and structural unit of life.
Bisa
what is genetic
Janet Reply
I join
Janet
what are the branchas of biology
Prisca Reply
zoology, ecology
Millicent
biochemistry,cytology,herpetology...etc
R0se
genetics, microbiology,botany and embryology
Muhammad
what is a cell
Kulunbawi Reply
cell is smallest unit of life. cells are often cell the building blocks of life...
Muhammad
the first twenty element
Orapinega Reply
what are the characteristics of living things?
R0se
growth,respiration,nutrition,sensitivity, movement,irritability, excretion,death.
Obinna
What is the difference between adaptation and competition in animals
Adeyemi Reply
What is biology
Adeyemi
it is a natural science stadey about living things
Zamiil
Biology is the bronch of science which deals with the study of life is called biology
Aziz
what is the x in 300 stands for?
Ogbudu Reply
the properties of life
Clarinda Reply
response to the environment, reproduction, homeostasis, growth,energy processing etc.....
Pushpam
hello.
Daniela
hi
MacPeter
Good
Thomas
what is reproduction
Tims
Reproduction is a fundamental feature of all known life,each individual organism exist as a result of re production.....or else Multiplying...
R0se
a complete virus particle known as
Darlington Reply
These are formed from identical protein subunitscalled capsomeres.
Pushpam
fabace family plant name
Pushpam Reply
in eukaryotes ...protein channel name which transport protein ...
Pushpam Reply
in bacteria ...chromosomal dna duplicate structure called
Pushpam
Got questions? Join the online conversation and get instant answers!
Jobilize.com Reply

Get the best Algebra and trigonometry course in your pocket!





Source:  OpenStax, Introductory statistics. OpenStax CNX. Aug 09, 2016 Download for free at http://legacy.cnx.org/content/col11776/1.26
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Introductory statistics' conversation and receive update notifications?

Ask