# 5.3 Binomial distribution - university of calgary - base content  (Page 5/30)

 Page 5 / 30

## Try it

A lacrosse team is selecting a captain. The names of all the seniors are put into a hat, and the first three that are drawn will be the captains. The names are not replaced once they are drawn (one person cannot be two captains). You want to see if the captains all play the same position. State whether this is binomial or not and state why.

This is not binomial because the names are not replaced, which means the probability changes for each time a name is drawn. This violates the condition of independence.

## References

“Access to electricity (% of population),” The World Bank, 2013. Available online at http://data.worldbank.org/indicator/EG.ELC.ACCS.ZS?order=wbapi_data_value_2009%20wbapi_data_value%20wbapi_data_value-first&sort=asc (accessed May 15, 2015).

“Distance Education.” Wikipedia. Available online at http://en.wikipedia.org/wiki/Distance_education (accessed May 15, 2013).

“NBA Statistics – 2013,” ESPN NBA, 2013. Available online at http://espn.go.com/nba/statistics/_/seasontype/2 (accessed May 15, 2013).

Newport, Frank. “Americans Still Enjoy Saving Rather than Spending: Few demographic differences seen in these views other than by income,” GALLUP® Economy, 2013. Available online at http://www.gallup.com/poll/162368/americans-enjoy-saving-rather-spending.aspx (accessed May 15, 2013).

Pryor, John H., Linda DeAngelo, Laura Palucki Blake, Sylvia Hurtado, Serge Tran. The American Freshman: National Norms Fall 2011 . Los Angeles: Cooperative Institutional Research Program at the Higher Education Research Institute at UCLA, 2011. Also available online at http://heri.ucla.edu/PDFs/pubs/TFS/Norms/Monographs/TheAmericanFreshman2011.pdf (accessed May 15, 2013).

“The World FactBook,” Central Intelligence Agency. Available online at https://www.cia.gov/library/publications/the-world-factbook/geos/af.html (accessed May 15, 2013).

“What are the key statistics about pancreatic cancer?” American Cancer Society, 2013. Available online at http://www.cancer.org/cancer/pancreaticcancer/detailedguide/pancreatic-cancer-key-statistics (accessed May 15, 2013).

## Chapter review

A statistical experiment can be classified as a binomial experiment if the following conditions are met:

1. There are a fixed number of trials, n .
2. There are only two possible outcomes, called "success" and, "failure" for each trial. The letter p denotes the probability of a success on one trial and q denotes the probability of a failure on one trial.
3. The n trials are independent and are repeated using identical conditions.

The outcomes of a binomial experiment fit a binomial probability distribution. The random variable X = the number of successes obtained in the n independent trials. The mean of X can be calculated using the formula μ = np , and the standard deviation is given by the formula σ = .

## Formula review

X ~ B ( n , p ) means that the discrete random variable X has a binomial probability distribution with n trials and probability of success p .

X = the number of successes in n independent trials

n = the number of independent trials

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

p = the probability of a success for any trial

q = the probability of a failure for any trial

p + q = 1

q = 1 – p

The mean of X is μ = np . The standard deviation of X is σ = $\sqrt{npq}$ .

Use the following information to answer the next eight exercises: The Higher Education Research Institute at UCLA collected data from 203,967 incoming first-time, full-time freshmen from 270 four-year colleges and universities in the U.S. 71.3% of those students replied that, yes, they believe that same-sex couples should have the right to legal marital status. Suppose that you randomly pick eight first-time, full-time freshmen from the survey. You are interested in the number that believes that same sex-couples should have the right to legal marital status.

In words, define the random variable X .

X = the number that reply “yes”

X ~ _____(_____,_____)

What values does the random variable X take on?

0, 1, 2, 3, 4, 5, 6, 7, 8

Construct the probability distribution function (PDF).

x P ( x )

On average ( μ ), how many would you expect to answer yes?

5.7

What is the standard deviation ( σ )?

What is the probability that at most five of the freshmen reply “yes”?

0.4151

What is the probability that at least two of the freshmen reply “yes”?

#### Questions & Answers

why does it makes sense to let the sewage disposal company in your town have a monopoly?
how might a monopoly affect price?
Janice
how might a monopoly affect prices?
Janice
The principle of Economic is one to be involved in any economic buying substance
what are the principle of economics?
What is (Qs)
What is (Qs) and (Qd)
Bigi
Quantity of supply and Quantity of demand
Dilshoda
Qs: Is quantity of supply and Qd: quantity of demand
Cabdikariim
give as me quantitys
ahmed
among all the definition of economics which of the definition is generally acceptable?
oche
i science that studies human behavior as a relationship between ends and scarcity that have alternative uses
ousman
okay......
oche
what are the principle of economics?
oche
what Make things scarce
why do we studied economic
Soudani
for the stability and growth of any reign.
Fayaz
what is macro economics.?
Fayaz
which part of economics is interesting..
Fayaz
how does economics define me
what are the factors that determines the demand and supply
sillah
what are the importance of Economics
tell me something very important about economics..
how may I solve arithmetic mean ,,,all example
what is agriculture
simple method of understanding cost concept
what is inflation
Inflation is a general increase in price levels
Zuko
is the action of inflating something
Abdifatah
inflation is the persistent increase in general price level of goods and services in an economy over a considerable period of time .
Tetteh
inflation is the general increase of a commodity in a particular period of time.
Turay
inflation is a general increase in price levels of commodities
shehu
what are the types of inflation?
Ebrima
inflation is the period of persistent rise in the general level of the price of goods services over time
Emmanuel
we have creeping inflation, demand pull inflation ,cost push inflation, and galloping inflation .
Emmanuel
I s Nigeria in any kind of in inflation? If yes which kind?
Martins
please can someone help me with the principles of economic?
Jonathan
and u
ahmed
no discassion just question
Aliraza
what is science and art economic
how can a location of a firm create difference between producers
what is monetary policy
joy
hello
Abdifatah
is a monetary from policy that's authorized of country encharces
Abdifatah
What would you say about the the mobility of enterprise as a factor of production?
how can I connect myself to this Ambrose platform
Got questions? Join the online conversation and get instant answers!