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Discrete distribution (playing card experiment)

Class Time:


    Student learning outcomes

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


  • One full deck of playing cards


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

  1. The theoretical 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 ten 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 [link] . Then calculate the relative frequency.
    x Frequency Relative Frequency
    0 __________ __________
    1 __________ __________
    2 __________ __________
    3 __________ __________
    4 __________ __________
    5 __________ __________
    6 __________ __________
    7 __________ __________
    8 __________ __________
    9 __________ __________
    10 __________ __________
  2. Calculate the following:
    1. x ¯ = ________
    2. s = ________
  3. Construct a histogram of the empirical data.
    This is a blank graph template. The x-axis is labeled Number of diamonds. The y-axis is labeled Relative frequency.

    Theoretical distribution

  1. Build the theoretical PDF chart based on the distribution in the Procedure section.
    x P ( x )
  2. Calculate the following:
    1. μ = ____________
    2. σ = ____________
  3. Construct a histogram of the theoretical distribution.
    This is a blank graph template. The x-axis is labeled Number of diamonds. The y-axis is labeled Probability.

Using the data


RF = relative frequency

Use the table from the Theoretical Distribution section to calculate the following answers. Round your answers to four decimal places.

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

Use the data from the Organize the Data section to calculate the following answers. Round your answers to four decimal places.

  • 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, 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.
  2. Describe the three most significant differences between the graphs or distributions of the theoretical and empirical distributions.
  3. Using your answers from questions 1 and 2, does it appear that the data fit the theoretical distribution? In complete sentences, explain why or why not.
  4. Suppose that the experiment had been repeated 500 times. Would you expect [link] or [link] to change, and how would it change? Why? Why wouldn’t the other table change?

Questions & Answers

Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
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
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
what school?
biomolecules are e building blocks of every organics and inorganic materials.
anyone know any internet site where one can find nanotechnology papers?
Damian Reply
sciencedirect big data base
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.
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
for teaching engĺish at school how nano technology help us
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
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?
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
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
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Source:  OpenStax, Introduction to statistics i - stat 213 - university of calgary - ver2015revb. OpenStax CNX. Oct 21, 2015 Download for free at http://legacy.cnx.org/content/col11874/1.3
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