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
what is variations in raman spectra for nanomaterials
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
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?
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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