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.
Supplies
One full deck of playing cards
Procedure
The experimental procedure is to pick one card from a deck of shuffled cards.
The theoretical 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 ten 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
[link] . Then calculate the relative frequency.
x
Frequency
Relative Frequency
0
__________
__________
1
__________
__________
2
__________
__________
3
__________
__________
4
__________
__________
5
__________
__________
6
__________
__________
7
__________
__________
8
__________
__________
9
__________
__________
10
__________
__________
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.
x
P (
x )
0
1
2
3
4
5
6
7
8
9
10
Calculate the following:
μ = ____________
σ = ____________
Construct a histogram of the theoretical distribution.
Using the data
Note
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.
Knowing that data vary, describe three similarities between the graphs and distributions of the theoretical and empirical distributions. Use complete sentences.
Describe the three most significant differences between the graphs or distributions of the theoretical and empirical distributions.
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.
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?
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?
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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