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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:

Names:

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.

Supplies:

  • One full deck of playing cards

Procedure

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 )} {}
    0
    1
    2
    3
    4
    5
    6
    7
    8
    9
    10
  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

where we get a research paper on Nano chemistry....?
Maira Reply
what are the products of Nano chemistry?
Maira Reply
There are lots of products of nano chemistry... Like nano coatings.....carbon fiber.. And lots of others..
learn
Even nanotechnology is pretty much all about chemistry... Its the chemistry on quantum or atomic level
learn
Google
da
no nanotechnology is also a part of physics and maths it requires angle formulas and some pressure regarding concepts
Bhagvanji
hey
Giriraj
Preparation and Applications of Nanomaterial for Drug Delivery
Hafiz Reply
revolt
da
Application of nanotechnology in medicine
what is variations in raman spectra for nanomaterials
Jyoti Reply
I only see partial conversation and what's the question here!
Crow Reply
what about nanotechnology for water purification
RAW Reply
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
Damian
yes that's correct
Professor
I think
Professor
Nasa has use it in the 60's, copper as water purification in the moon travel.
Alexandre
nanocopper obvius
Alexandre
what is the stm
Brian Reply
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
Rafiq
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
Damian
How we are making nano material?
LITNING Reply
what is a peer
LITNING Reply
What is meant by 'nano scale'?
LITNING Reply
What is STMs full form?
LITNING
scanning tunneling microscope
Sahil
how nano science is used for hydrophobicity
Santosh
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
Rafiq
what is differents between GO and RGO?
Mahi
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
Rafiq
if virus is killing to make ARTIFICIAL DNA OF GRAPHENE FOR KILLED THE VIRUS .THIS IS OUR ASSUMPTION
Anam
analytical skills graphene is prepared to kill any type viruses .
Anam
Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
Hafiz
what is Nano technology ?
Bob Reply
write examples of Nano molecule?
Bob
The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
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
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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