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This module allows students to explore concepts related to discrete random variables through the use of a simple playing card experiment. Students will compare empirical data to a theoretical distribution to determine if the experiment fist a discrete distribution. This lab involves the concept of long-term probabilities.

Class Time:


Student learning outcomes:

  • The student will compare empirical data and a theoretical distribution to determine if everyday experiment fits a discrete distribution.
  • The student will demonstrate an understanding of long-term probabilities.


  • One full deck of playing cards


The experiment procedure is to pick one card from a deck of shuffled cards.

  1. The theorectical probability of picking a diamond from a deck is: _________
  2. Shuffle a deck of cards.
  3. Pick one card from it.
  4. Record whether it was a diamond or not a diamond.
  5. Put the card back and reshuffle.
  6. Do this a total of 10 times
  7. Record the number of diamonds picked.
  8. Let X = number of diamonds. Theoretically, X ~ B ( _____,_____ )

Organize the data

  1. Record the number of diamonds picked for your class in the chart below. Then calculate the relative frequency.
    x Frequency Relative Frequency
    0 __________ __________
    1 __________ __________
    2 __________ __________
    3 __________ __________
    4 __________ __________
    5 __________ __________
    6 __________ __________
    7 __________ __________
    8 __________ __________
    9 __________ __________
    10 __________ __________
  2. Calculate the following:
    • x =
    • s =
  3. Construct a histogram of the empirical data.
    Blank graph with relative frequency on the vertical axis and number of diamonds on the horizontal axis.

Theoretical distribution

  1. Build the theoretical PDF chart based on the distribution in the Procedure section above.
    x size 12{x} {} P x size 12{P left (x=x right )} {}
  2. Calculate the following:
    • μ = size 12{μ={}} {} ____________
    • σ = size 12{σ={}} {} ____________
  3. Construct a histogram of the theoretical distribution.
    Blank graph with relative frequency on the vertical axis and number of diamonds on the horizontal axis.

Using the data

Calculate the following, rounding to 4 decimal places:

RF = relative frequency

Use the table from the section titled "Theoretical Distribution" here:

  • P ( x = 3 ) =
  • P ( 1 < x < 4 ) =
  • P ( x 8 ) =

Use the data from the section titled "Organize the Data" here:

  • RF ( x = 3 ) =
  • RF ( 1 < x < 4 ) =
  • RF ( x 8 ) =

Discussion questions

For questions 1. and 2., think about the shapes of the two graphs, the probabilities and the relative frequencies, the means, and the standard deviations.

  1. Knowing that data vary, describe three similarities between the graphs and distributions of the theoretical and empirical distributions. Use complete sentences. (Note: These answersmay vary and still be correct.)
  2. Describe the three most significant differences between the graphs or distributions of the theoretical and empirical distributions. (Note: These answers may vary and still becorrect.)
  3. Using your answers from the two previous questions, does it appear that the data fit the theoretical distribution? In 1 - 3 complete sentences, explain why or why not.
  4. Suppose that the experiment had been repeated 500 times. Which table (from "Organize the data" and "Theoretical Distributions") would you expect to change (and how would it change)? Why? Why wouldn’t the other table change?

Questions & Answers

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
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
characteristics of micro business
Do somebody tell me a best nano engineering book for beginners?
s. Reply
what is fullerene does it is used to make bukky balls
Devang Reply
are you nano engineer ?
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.
what is the actual application of fullerenes nowadays?
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.
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.
is Bucky paper clear?
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.
Do you know which machine is used to that process?
how to fabricate graphene ink ?
for screen printed electrodes ?
What is lattice structure?
s. Reply
of graphene you mean?
or in general
in general
Graphene has a hexagonal structure
On having this app for quite a bit time, Haven't realised there's a chat room in it.
what is biological synthesis of nanoparticles
Sanket Reply
what's the easiest and fastest way to the synthesize AgNP?
Damian Reply
types of nano material
abeetha Reply
I start with an easy one. carbon nanotubes woven into a long filament like a string
many many of nanotubes
what is the k.e before it land
what is the function of carbon nanotubes?
I'm interested in nanotube
what is nanomaterials​ and their applications of sensors.
Ramkumar Reply
what is nano technology
Sravani Reply
what is system testing?
preparation of nanomaterial
Victor Reply
Yes, Nanotechnology has a very fast field of applications and their is always something new to do with it...
Himanshu Reply
good afternoon madam
what is system testing
what is the application of nanotechnology?
In this morden time nanotechnology used in many field . 1-Electronics-manufacturad IC ,RAM,MRAM,solar panel etc 2-Helth and Medical-Nanomedicine,Drug Dilivery for cancer treatment etc 3- Atomobile -MEMS, Coating on car etc. and may other field for details you can check at Google
anybody can imagine what will be happen after 100 years from now in nano tech world
after 100 year this will be not nanotechnology maybe this technology name will be change . maybe aftet 100 year . we work on electron lable practically about its properties and behaviour by the different instruments
name doesn't matter , whatever it will be change... I'm taking about effect on circumstances of the microscopic world
how hard could it be to apply nanotechnology against viral infections such HIV or Ebola?
silver nanoparticles could handle the job?
not now but maybe in future only AgNP maybe any other nanomaterials
I'm interested in Nanotube
this technology will not going on for the long time , so I'm thinking about femtotechnology 10^-15
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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1 It is estimated that 30% of all drivers have some kind of medical aid in South Africa. What is the probability that in a sample of 10 drivers: 3.1.1 Exactly 4 will have a medical aid. (8) 3.1.2 At least 2 will have a medical aid. (8) 3.1.3 More than 9 will have a medical aid.
Nerisha Reply

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Source:  OpenStax, Collaborative statistics. OpenStax CNX. Jul 03, 2012 Download for free at http://cnx.org/content/col10522/1.40
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