<< Chapter < Page Chapter >> Page >
Basic directions on exploring distributions.

Discrete and continuous random variables using spreadsheets

In this section we will discuss techniques using spreadsheet for exploring discrete and continuous variables particularly, creating probability tables, calculating the binomial probability functions, and then graphing probabilities.

Creating probability tables

If you are generating your data and have your outcomes, or if you know the probabilities of the outcomes you can generate a table of probabilities by using a formula. You will create a three column table with the “possible outcomes” in the first column, the probability of that outcome in the second column, and in the third column you will create the formula multiplying column one by column two or the “expected value”. Using the example in the book on finding the expected value of the number of times a baby’s crying will wakes its mother after midnight. The data below is from a sample of 50 mothers’ responses to the question how many times did your baby’s crying awake you after midnight? 2 mothers said “0” times, 11 mothers said “1” time, 23 mothers said “2” times, 9 mothers said “3” times, 4 mothers said “4” times, 1 mother said “5” times,

Number of times baby’s cry awoke mother after midnight

Number of Mothers who selected
0 P( x =0) = 2/50
1 P( x =1) = 11/50
2 P( x =2) = 23/50
3 P( x =3) = 9/50
4 P( x =4) = 4/50
5 P( x =5) = 1/50

Using the formulas shown in the google spreadsheet below you can calculate the expected value and create a chart of probabilities.

Calculating the binomial probability function

Both Excel and Google Spreadsheet will calculate Binomial Probability functions. The Excel formula for a particular value is =BINOM.DIST(x of successes , sample size , probability of success,false) for a cumulative probability it is =BINOM.DIST(x of successes , sample size , probability of success,true) The Google Spreadsheet formula is given below in the spreadsheet. The setup is the same but there isn’t a “period between binom and dist. The other difference is that instead of using true and false for cumulative probability, Google uses 0 for false and 1 for true. Using the example problem from the book: It has been stated that about 41% of adult workers have a high school diploma but do not pursue any further education. If 20 adult workers are randomly selected, find the probability that at most 12 of them have a high school diploma but do not pursue any further education. How many adult workers do you expect to have a high school diploma but do not pursue any further education?

Note that the answer to the question is asking for a cumulative frequency for 12 or less people out of the sample of twenty. The answer is in column C, row 14, .9738. We would expect that out of a sample size of 20 people a probability of 97.38% that 12 or less people would have a high school diploma and did not pursue further education.

To graph probability functions, we have found that “Statistics Online Computational Resources (SOCR)” has a wonderful site with tools for statistics. If you go to http://socr.ucla.edu/htmls/SOCR_Distributions.html in the dropdown menu for SOCR distribution you will find many types of distributions. For the example we just completed you would use Binomial Distribution; set the number of trials to 20 and the success probability to .41 (as stated in the problem and the following image will appear. Everything you would want to know.

Continuous uniform distributions and normal distributions:

This same tool can be used to generate continuous uniform distributions, and normal distributions. For continuous uniform distributions you will need to know and enter the lower and upper limits of the data plus the range of data that you wish to calculate the probability. In the example below I have used the problem from the book: Suppose we want to find the area between f(x) = 1/20 and the x-axis where 4<x<15 the following image would be produced with the Red shaded density (probability) = 0.55

For a normal distribution, you will need to have your mean and standard deviation and again your right and left cut off values. Replicating Figure 5.3 in your text, I would use 0 as the mean, 1 as the standard deviation and 1 as my left cut off and 2 as my right cut off. See below. I now have the density or probability for a value between 1 and 2 (0.125905)

Optional classroom exercise:

At your computer, try to use some of these tools to work out homework problems or check homework that you have completed to see if the results are the same or similar.

Questions & Answers

Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
Stoney Reply
why we need to study biomolecules, molecular biology in nanotechnology?
Adin Reply
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
Adin
why?
Adin
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
anyone know any internet site where one can find nanotechnology papers?
Damian Reply
research.net
kanaga
sciencedirect big data base
Ernesto
Introduction about quantum dots in nanotechnology
Praveena Reply
what does nano mean?
Anassong Reply
nano basically means 10^(-9). nanometer is a unit to measure length.
Bharti
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
Damian Reply
absolutely yes
Daniel
how to know photocatalytic properties of tio2 nanoparticles...what to do now
Akash Reply
it is a goid question and i want to know the answer as well
Maciej
characteristics of micro business
Abigail
for teaching engĺish at school how nano technology help us
Anassong
Do somebody tell me a best nano engineering book for beginners?
s. Reply
there is no specific books for beginners but there is book called principle of nanotechnology
NANO
what is fullerene does it is used to make bukky balls
Devang Reply
are you nano engineer ?
s.
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
Tarell
what is the actual application of fullerenes nowadays?
Damian
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
Tarell
what is the Synthesis, properties,and applications of carbon nano chemistry
Abhijith Reply
Mostly, they use nano carbon for electronics and for materials to be strengthened.
Virgil
is Bucky paper clear?
CYNTHIA
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
NANO
so some one know about replacing silicon atom with phosphorous in semiconductors device?
s. Reply
Yeah, it is a pain to say the least. You basically have to heat the substarte up to around 1000 degrees celcius then pass phosphene gas over top of it, which is explosive and toxic by the way, under very low pressure.
Harper
Do you know which machine is used to that process?
s.
how to fabricate graphene ink ?
SUYASH Reply
for screen printed electrodes ?
SUYASH
What is lattice structure?
s. Reply
of graphene you mean?
Ebrahim
or in general
Ebrahim
in general
s.
Graphene has a hexagonal structure
tahir
On having this app for quite a bit time, Haven't realised there's a chat room in it.
Cied
what is biological synthesis of nanoparticles
Sanket Reply
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
Privacy Information Security Software Version 1.1a
Good
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, Collaborative statistics using spreadsheets. OpenStax CNX. Jan 05, 2016 Download for free at http://legacy.cnx.org/content/col11521/1.23
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Collaborative statistics using spreadsheets' conversation and receive update notifications?

Ask