# 0.6 Central limit theorem: central limit theorem lab i (edited:

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Labs changed to incorporate mini-tabs.

Class Time:

Name:

## Student learning outcomes:

• The student will examine properties of the Central Limit Theorem.

## Collect the data

• Using the random number generator in minitab, simulate the tossing of a single die 60 times. Calc ->Random Data ->Integer
• Using Stat ->Tables ->Tally, summarize the data
• Construct a histogram using Minitab and then sketch the graph using a ruler and pencil. Scale the axes.
• Caluclate the following:
• ## A

$\overline{x}$ =
• ## B

$s$ =
• ## C

$n=1$ (single die)
• Draw a smooth curve through the tops of the bars of the histogram. Use 1 – 2 complete sentences to describe the general shape of the curve.

## Collecting averages of pairs

Repeat steps 1 - 5 (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 50 rows with two columns. Then use the Calc ->Row Statistics and select mean. Then use Stats ->Tables ->Tally to summarize the data.

• Construct a histogram. Scale the axes using the same scaling you did for the section titled "Collecting the Data". Sketch the graph using a ruler and a pencil.
• Calculate the following:
• ## A

$\overline{x}$ =
• ## B

$s$ =
• ## C

$n=2$ (surveying one person at a time)
• Draw a smooth curve through tops of the bars of the histogram. Use 1 – 2 complete sentences to describe the general shape of the curve.

## Collecting averages of groups of five

Repeat steps 1 – 5 (of part I) with one exception. Instead of recording the value for a single die, record the average value for each of the 50 groups of 5 die tosses.

• Generate fifty groups of 5 die tosses. Record the values of the average of their value.
• Construct a histogram. Scale the axes using the same scaling you did for section titled "Collect the Data". Sketch the graph using a ruler and a pencil.
• Calculate the following:
• ## A

$\overline{x}$ =
• ## B

$s$ =
• ## C

$n=5$ (surveying five people at a time)
• Draw a smooth curve through tops of the bars of the histogram. Use 1 – 2 complete sentences to describe the general shape of the curve.

## Collecting averages of groups of 20

Repeat steps 1 – 5 (of part I) recording the average value for each of the 50 groups of 20 die tosses.

• Generate fifty groups of 20 die tosses. Record the values of the average of their value.
• Construct a histogram. Scale the axes using the same scaling you did for section titled "Collect the Data". Sketch the graph using a ruler and a pencil.
• Calculate the following
• Draw a smooth curve through tops of the bars of the histogram. Use 1 – 2 complete sentences to describe the general shape of the curve.

## Discussion questions

• As $n$ changed, why did the shape of the distribution of the data change? Use 1 – 2 complete sentences to explain what happened.
• In the section titled "Collect the Data", what was the approximate distribution of the data? $X$ ~
• In the section titled "Collecting Averages of Groups of Five", what was the approximate distribution of the data? $X$ ~
• In the section titled "Collecting Averages of Groups of Twenty", what was the approximate distribution of the data? $X$ ~
• In 1 – 2 complete sentences, explain any differences in your answers to previous three questions.

#### Questions & Answers

where we get a research paper on Nano chemistry....?
what are the products of Nano chemistry?
There are lots of products of nano chemistry... Like nano coatings.....carbon fiber.. And lots of others..
learn
Even nanotechnology is pretty much all about chemistry... Its the chemistry on quantum or atomic level
learn
da
no nanotechnology is also a part of physics and maths it requires angle formulas and some pressure regarding concepts
Bhagvanji
Preparation and Applications of Nanomaterial for Drug Delivery
revolt
da
Application of nanotechnology in medicine
what is variations in raman spectra for nanomaterials
I only see partial conversation and what's the question here!
what about nanotechnology for water purification
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
Damian
yes that's correct
Professor
I think
Professor
Nasa has use it in the 60's, copper as water purification in the moon travel.
Alexandre
nanocopper obvius
Alexandre
what is the stm
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
Rafiq
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
Damian
How we are making nano material?
what is a peer
What is meant by 'nano scale'?
What is STMs full form?
LITNING
scanning tunneling microscope
Sahil
how nano science is used for hydrophobicity
Santosh
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
Rafiq
if virus is killing to make ARTIFICIAL DNA OF GRAPHENE FOR KILLED THE VIRUS .THIS IS OUR ASSUMPTION
Anam
analytical skills graphene is prepared to kill any type viruses .
Anam
Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
Hafiz
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
how did you get the value of 2000N.What calculations are needed to arrive at it
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