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Using minitab, students will explore the central limit theorem.

Central Limit Theorem Lab

Name: ___________________________

Student learning outcomes:

The student will examine properties of the Central Limit Theorem.

Theoretical distribution: tossing a single die

1. Is the distribution continuous or discrete? __________________

2. In words, state the theoretical distribution for the tossing of a single die?

X~ _____________________________________________

3. Calculate μ = _____________________________________________________________(indicate the formula)

4. Calculate σ = _____________________________________________________________(indicate the formula)

Collect the data

1. Using the random number generator in Minitab, simulate the tossing of a single die 360 times.

Calc ->Random Data ->Integer.

2. Construct a histogram using Minitab and include it with this lab. Be sure that you label the graph and axis.

3. Calculate the following: (include the session window)

x ¯ size 12{ {overline {x}} } {} = ______________ s = ______________ n = 1 (single die)

4. Draw a smooth curve through the tops of the bars of the histogram. Use 1 – 2 complete sentences, describe the general shape of the curve.

Collecting averages of pairs

Repeat step #1 (of the section above titled "Collect the Data") with one exception. Instead of recording the value of a single die, record the average of two dice. Use Minitab and generate 360 rows with two columns. Then use the Calc ->Row Statistics and select mean. This will give you a column with the ‘average’ of the two tosses.

1. Construct a histogram. Scale the axes using the same scaling and labeling for the axis as you did for the first graph and include it with this lab. (This is done by selecting both the original data column and the mean2 column to graph. Then select multiple graphs → separate graphs → same x-scale. This will redraw your first graph, however the computer needs that graph as a reference to draw the second.)

2. Calculate the following:

x ¯ size 12{ {overline {x}} } {} = ______________ s = ______________ n = 2 (a pair of dice)

3. Draw a smooth curve through tops of the bars of the histogram. Use 1 – 2 complete sentences, describe the general shape of the curve.

Collecting averages of groups of five

Repeat step #1 (of the section above titled "Collect the Data") with one exception. Instead of recording the value of a single die, record the average of five dice. Use Minitab and generate 360 rows with five columns. Then use the Calc ->Row Statistics and select mean. This will give you a column with the ‘average’ of the five tosses.

1. Construct a histogram. Scale the axes using the same scaling and labeling for the axis as you did for the first graph and include it with this lab. (Again you need to graph both the first data set with this as multiple graphs.)

2. Calculate the following:

x ¯ size 12{ {overline {x}} } {} = ______________ s = ______________ n = 5 (5 dice)

3. Draw a smooth curve through tops of the bars of the histogram. Use 1 – 2 complete sentences, describe the general shape of the curve.

Collecting averages of groups of 20

Repeat step #1 (of the section above titled "Collect the Data") with one exception. Instead of recording the value of a single die, record the average of two dice. Use Minitab and generate 360 rows with twenty columns. Then use the Calc ->Row Statistics and select mean. This will give you a column with the ‘average’ of the twenty tosses.

1. Construct a histogram. Scale the axes using the same scaling and labeling for the axis as you did for the first graph and include it with this lab. (Again you need to graph both the first data set with this as multiple graphs.)

2. Calculate the following:

x ¯ size 12{ {overline {x}} } {} = ______________ s = ______________ n = 20 (20 dice)

3. Draw a smooth curve through tops of the bars of the histogram. Use 1 – 2 complete sentences, describe the general shape of the curve.

Discussion questions:

1. As n (the number of dice being averaged) changed, how did the shape of the graph change? (Be sure you have the same x axis for all graphs or you will not be able to correctly answer this question.) Use 1 – 2 complete sentences to explain what happened.

2. Looking at the values for the sample mean and standard deviation, explain what happens as n increases. Use 1 – 2 complete sentences to explain what happened.

3. State the Central Limit Theorem. How do your simulations demonstrate this theorem? Use 3 – 4 complete sentences

Questions & Answers

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
anyone know any internet site where one can find nanotechnology papers?
Damian Reply
research.net
kanaga
sciencedirect big data base
Ernesto
Introduction about quantum dots in nanotechnology
Praveena Reply
what does nano mean?
Anassong Reply
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?
Damian Reply
absolutely yes
Daniel
how to know photocatalytic properties of tio2 nanoparticles...what to do now
Akash Reply
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?
s. Reply
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
Devang Reply
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
Abhijith Reply
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?
s. Reply
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 ?
SUYASH Reply
for screen printed electrodes ?
SUYASH
What is lattice structure?
s. Reply
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
what is biological synthesis of nanoparticles
Sanket Reply
what's the easiest and fastest way to the synthesize AgNP?
Damian Reply
China
Cied
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Source:  OpenStax, Collaborative statistics (with edits: teegarden). OpenStax CNX. Jul 20, 2009 Download for free at http://legacy.cnx.org/content/col10561/1.3
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