# 7.9 Lab 2: central limit theorem (cookie recipes)

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Class Time:

Names:

## Student learning outcomes:

• The student will demonstrate and compare properties of the Central Limit Theorem.

## Given:

$X$ = length of time (in days) that a cookie recipe lasted at the Olmstead Homestead. (Assume that each of the different recipes makes the same quantity of cookies.)

Recipe # $X$ Recipe # $X$ Recipe # $X$ Recipe # $X$
1 1 16 2 31 3 46 2
2 5 17 2 32 4 47 2
3 2 18 4 33 5 48 11
4 5 19 6 34 6 49 5
5 6 20 1 35 6 50 5
6 1 21 6 36 1 51 4
7 2 22 5 37 1 52 6
8 6 23 2 38 2 53 5
9 5 24 5 39 1 54 1
10 2 25 1 40 6 55 1
11 5 26 6 41 1 56 2
12 1 27 4 42 6 57 4
13 1 28 1 43 2 58 3
14 3 29 6 44 6 59 6
15 2 30 2 45 2 60 5

Calculate the following:

• ${\mu }_{x}=$
• ${\sigma }_{x}=$

## Collect the data

Use a random number generator to randomly select 4 samples of size $n=5$ from the given population. Record your samples below. Then, for each sample, calculate the mean to the nearesttenth. Record them in the spaces provided. Record the sample means for the rest of the class.

1. Complete the table:
Sample 1 Sample 2 Sample 3 Sample 4 Sample means from other groups:
Means: $\overline{x}=$ $\overline{x}=$ $\overline{x}=$ $\overline{x}=$
2. Calculate the following:
• $\overline{x}=$
• ${s}_{\overline{x}}=$
3. Again, use a random number generator to randomly select 4 samples from the population. This time, make the samples of size $n=\text{10}$ . Record the samples below. As before, for each sample, calculate the mean to the nearest tenth. Record them in the spaces provided. Record the sample means for the rest of the class.
Sample 1 Sample 2 Sample 3 Sample 4 Sample means from other groups:
Means: $\overline{x}=$ $\overline{x}=$ $\overline{x}=$ $\overline{x}=$
4. Calculate the following:
• $\overline{x}=$
• ${s}_{\overline{x}}=$
5. For the original population, construct a histogram. Make intervals with bar width = 1 day. Sketch the graph using a ruler and pencil. Scale the axes.
6. 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.

## Repeat the procedure for n=5

1. For the sample of $n=\text{5 days}$ averaged together, construct a histogram of the averages (your means together with the means of the other groups). Make intervals with $\text{bar widths =}\frac{1}{2}\text{day}$ . Sketch the graph using a ruler and pencil. Scale the axes.
2. 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.

## Repeat the procedure for n=10

1. For the sample of $n=\text{10 days}$ averaged together, construct a histogram of the averages (your means together with the means of the other groups). Make intervals with $\text{bar widths =}\frac{1}{2}\text{day}$ . Sketch the graph using a ruler and pencil. Scale the axes.
2. 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.

## Discussion questions

1. Compare the three histograms you have made, the one for the population and the two for the sample means. In three to five sentences, describe the similarities and differences.
2. State the theoretical (according to the CLT) distributions for the sample means.
• $n=5$ : $\overline{X}$ ~
• $n=10$ : $\overline{X}$ ~
3. Are the sample means for $\text{n = 5}$ and $\text{n = 10}$ “close” to the theoretical mean, ${\mu }_{x}$ ? Explain why or why not.
4. Which of the two distributions of sample means has the smaller standard deviation? Why?
5. As n changed, why did the shape of the distribution of the data change? Use 1 – 2 complete sentences to explain what happened.
This lab was designed and contributed by Carol Olmstead.

#### 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
1 It is estimated that 30% of all drivers have some kind of medical aid in South Africa. What is the probability that in a sample of 10 drivers: 3.1.1 Exactly 4 will have a medical aid. (8) 3.1.2 At least 2 will have a medical aid. (8) 3.1.3 More than 9 will have a medical aid.