3.12 Probability topics: probability lab (edited: teegarden)

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This module presents students with a lab exercise allowing them to apply their understanding of Probability. Using a Minitab simulation, students will compare theoretical probabilities with experimental probabilities as it relates to dice. They will also investigate the effect of sample size.

Probability Lab

I. student learning outcomes:

• The student will calculate theoretical and empirical probabilities.

• The student will appraise the differences between the two types of probabilities.

• The student will demonstrate an understanding of long-term probabilities.

Ii. theoretical probability for the sum of two dice

Begin by looking at Theoretical probabilities for the sum of two dice. Let the value in the first row be the result for Die 1 and the value in the first column be the value for Die 2. Input the sum of the corresponding row and column in each box.

 + 1 2 3 4 5 6 1 2 3 4 5 6

Using the following table, record the theoretical probabilities.

 Sum 2 3 4 5 6 7 8 9 10 11 12 Count Probability

Using the table above, determine the following theoretical probabilities

1. P(sum less than 5) = _________________

2. P(sum at least 9) = _________________

3. P(sum at most 6) = _________________

4. P(sum more than 7) = _________________

5. P(sum between 3 and 8) = _________________

6. P(sum less than 11) = _________________

Iii. experimental (empirical) probability for the sum of two dice

Rolling the dice Using Minitab, simulate rolling two dice 360 times and finding the sum. Use Calc → Random Data → Integer, 360 rows and save in die 1, die 2.

Then use the Calc → Row Statistics. Select Sum, the two die columns and save in Sum Use Stat → Tables → Tally to summarize the data.

Record the experimental probabilities:

 Sum 2 3 4 5 6 7 8 9 10 11 12 Count Probability

Using the table above, determine the following experimental probabilities

1. P(sum less than 5) = _________________

2. P(sum at least 9) = _________________

3. P(sum at most 6) = _________________

4. P(sum more than 7) = _________________

5. P(sum between 3 and 8) = _________________

6. P(sum less than 11) = _________________

Iv. essay questions (on a separate sheet of paper, answer these questions in complete sentences.)

1. How do the empirical probabilities compare to the theoretical probabilities? (You may wish to convert the probabilities to percentages for ease of comparison.)

2. If you increased the number of times you rolled the dice to 720, would the empirical probability values change? Why?

Rerun the simulation and record your results.

 Sum 2 3 4 5 6 7 8 9 10 11 12 Count Probability

3. Did the increase in the number of trials cause the empirical probabilities and theoretical probabilities to be closer together or farther apart? Why? (You may wish to convert the probabilities to percentages for ease of comparison.)

ATTACH THE SESSION WINDOW WITH YOUR RESULTS AND THE ESSAY ANSWERS TO THIS COVER SHEET.

what is Nano technology ?
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?
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
why we need to study biomolecules, molecular biology in nanotechnology?
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
why?
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
anyone know any internet site where one can find nanotechnology papers?
research.net
kanaga
sciencedirect big data base
Ernesto
Introduction about quantum dots in nanotechnology
what does nano mean?
nano basically means 10^(-9). nanometer is a unit to measure length.
Bharti
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
absolutely yes
Daniel
how to know photocatalytic properties of tio2 nanoparticles...what to do now
it is a goid question and i want to know the answer as well
Maciej
characteristics of micro business
Abigail
for teaching engĺish at school how nano technology help us
Anassong
Do somebody tell me a best nano engineering book for beginners?
there is no specific books for beginners but there is book called principle of nanotechnology
NANO
what is fullerene does it is used to make bukky balls
are you nano engineer ?
s.
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
Mostly, they use nano carbon for electronics and for materials to be strengthened.
Virgil
is Bucky paper clear?
CYNTHIA
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
NANO
so some one know about replacing silicon atom with phosphorous in semiconductors device?
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?
s.
how to fabricate graphene ink ?
for screen printed electrodes ?
SUYASH
What is lattice structure?
of graphene you mean?
Ebrahim
or in general
Ebrahim
in general
s.
Graphene has a hexagonal structure
tahir
On having this app for quite a bit time, Haven't realised there's a chat room in it.
Cied
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