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.
The theorectical probability of picking a diamond from a deck is:
$\_\_\_\_\_\_\_\_\_$
Shuffle a deck of cards.
Pick one card from it.
Record whether it was a diamond or not a diamond.
Put the card back and reshuffle.
Do this a total of 10 times
Record the number of diamonds picked.
Let
$X=$ number of diamonds. Theoretically,
$X$ ~
$B(\_\_\_\_\_,\_\_\_\_\_)$
Organize the data
Record the number of diamonds picked for your class in the chart below. Then calculate the
relative frequency.
x
Frequency
Relative Frequency
0
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Calculate the following:
$\overline{x}$ =
$s$ =
Construct a histogram of the empirical data.
Theoretical distribution
Build the theoretical PDF chart based on the distribution in the Procedure section above.
$x$
$P\left(x\right)$
0
1
2
3
4
5
6
7
8
9
10
Calculate the following:
$\mu =$$\text{\_\_\_\_\_\_\_\_\_\_\_\_}$
$\sigma =$$\text{\_\_\_\_\_\_\_\_\_\_\_\_}$
Construct a histogram of the theoretical distribution.
Using the data
Calculate the following, rounding to 4 decimal places:
RF = relative frequency
Use the table from the section titled "Theoretical Distribution" here:
$P(x=3)=$
$P(1<x<4)=$
$P(x\ge 8)=$
Use the data from the section titled "Organize the Data" here:
$\mathrm{RF}(x=3)=$
$\mathrm{RF}(1<x<4)=$
$\mathrm{RF}(x\ge 8)=$
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.
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.)
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.)
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.
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?
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
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?
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
Azam
anybody can imagine what will be happen after 100 years from now in nano tech world
Prasenjit
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
Azam
name doesn't matter , whatever it will be change... I'm taking about effect on circumstances of the microscopic world
Prasenjit
how hard could it be to apply nanotechnology against viral infections such HIV or Ebola?
Damian
silver nanoparticles could handle the job?
Damian
not now but maybe in future only AgNP maybe any other nanomaterials
Azam
Hello
Uday
I'm interested in Nanotube
Uday
this technology will not going on for the long time , so I'm thinking about femtotechnology 10^-15
Prasenjit
how did you get the value of 2000N.What calculations are needed to arrive at it
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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.