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.
Complete the table:
Sample 1
Sample 2
Sample 3
Sample 4
Sample means from other groups:
Means:
$\overline{x}=$
$\overline{x}=$
$\overline{x}=$
$\overline{x}=$
Calculate the following:
$\overline{x}=$
${s}_{\overline{x}}=$
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:
$\overline{x}=$
$\overline{x}=$
$\overline{x}=$
$\overline{x}=$
Calculate the following:
$\overline{x}=$
${s}_{\overline{x}}=$
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.
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
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.
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
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.
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
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.
State the theoretical (according to the CLT) distributions for the sample means.
$n=5$ :
$\overline{X}$ ~
$n=10$ :
$\overline{X}$ ~
Are the sample means for
$\text{n = 5}$ and
$\text{n = 10}$ “close” to the theoretical mean,
${\mu}_{x}$ ?
Explain why or why not.
Which of the two distributions of sample means has the smaller standard deviation? Why?
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.
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?
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
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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.