# 7.5 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:

1. μ x = _______
2. σ x = _______

## Collect the data

Use a random number generator to randomly select four samples of size n = 5 from the given population. Record your samples in [link] . Then, 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.

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:
1. $\overline{x}$ = _______
2. s $\overline{x}$ = _______
3. Again, use a random number generator to randomly select four samples from the population. This time, make the samples of size n = 10. Record the samples in [link] . 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:
1. $\overline{x}$ = ______
2. s $\overline{x}$ = ______
5. For the original population, construct a histogram. Make intervals with a bar width of one 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 one to two complete sentences to describe the general shape of the curve.

## Repeat the procedure for n = 5

1. For the sample of n = 5 days averaged together, construct a histogram of the averages (your means together with the means of the other groups). Make intervals with bar widths of $\frac{1}{2}$ a 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 one to two complete sentences to describe the general shape of the curve.

## Repeat the procedure for n = 10

1. For the sample of n = 10 days averaged together, construct a histogram of the averages (your means together with the means of the other groups). Make intervals with bar widths of $\frac{1}{2}$ a 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 one to two 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.
1. n = 5: $\overline{x}$ ~ _____(_____,_____)
2. n = 10: $\overline{x}$ ~ _____(_____,_____)
3. Are the sample means for n = 5 and n = 10 “close” to the theoretical mean, μ 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 one to two complete sentences to explain what happened.

where do I start
in a large restaurant an average of every 7 customers ask for water with the their meal. A random sample of 12 customers is selected, find the probability that exactly 6 ask for water with their meal
any body with idea
Rufai
conditional probability
Ramesh
Rufai
iam really sorry. it's been long since I used these things. I just gave you a hint though
Ramesh
ok
Rufai
this follows binomial distribution. p(X=6)=12C6*(0.6)^6*0.4^6 use this formula n find.
syeda
can you explain the cosidered variable in the formula
Divya
x is variable wich is exactly 6 costumers
syeda
n is number of customers
syeda
ncx*p^X*q^X?
Divya
q^n-x
syeda
oh right !!! thanks yaar
Divya
I agree with Seyda too
Hoshyar
I agree with Syeda too
Hoshyar
7/12 =0.58is it?
yousaf
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yousaf
r8
khalid
what is descriptive statistic
Descriptive statistics are brief descriptive coefficients that summarize a given data set, which can be either a representation of the entire or a sample of a population. Descriptive statistics are broken down into measures of central tendency and measures of variability (spread).
Divya
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Divya
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Divya
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Ramesh
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Divya
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Anest
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Divya
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Anest
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Giannis
Hi
Makhosi
how u doing
Muhid
the upper quartile of the population 10,12,14,16,18,20,25,15,11,11,17,is................?
Gach
The probability range is 0 to 1... but why we take it 0 to 1....
because in probability 1 means success and 0 means failure and it cnnt be more or less than 1 and 0.
syeda
b/c v hv mazimum probibliy 1 and minimum which is.no.probiblity is 0.so.v hv the range from 0 to 1
khalid
the size of a set is greeter than its subset
Hoshyar
The probability of an event will not be less than 0.  This is because 0 is impossible (sure that something will not happen).The probability of an event will not be more than 1. This is because 1 is certain that something will happen
Divya
what do they mean in a question when you are asked to find P40 and P88
Mani
hi
Mehri
you're asked to find page 40 and page 88 on that particular book.
Joseph
hi
ravi
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ravi
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omar
No problem) By the way. I NEED a program For statistical data analysis. Any suggestion?
Mani
Eviews will help u
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Okonkwo
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ravi
Hi guys ,actually I have dicovered that the P40 and P88 means finding the 40th and 88th percentiles 😌..
Megrina
who can explain the euclidian distance
ravi
I am fresh student of statistics (BS) plz guide me best app or best website relative to stat topics
Noman
IMAGESNEWSVIDEOS A Dictionary of Computing. measures of location Quantities that represent the average or typical value of a random variable (compare measures of variation). They are either properties of a probability distribution or computed statistics of a sample. Three important measures are the mean, median, and mode.
define the measures of location
IMAGESNEWSVIDEOS A Dictionary of Computing. measures of location Quantities that represent the average or typical value of a random variable (compare measures of variation). They are either properties of a probability distribution or computed statistics of a sample. Three important measures are th
Ahmed
hi i have a question....
what is confidence interval estimate and its formula in getting it
discuss the roles of vital and health statistic in the planning of health service of the community
given that the probability of
BITRUS
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Rufai
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Bratit
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yousaf
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Bratit
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Divya
uses in health policy and health research
Divya
1) social inequalities I health 2) Trends in mortality
Divya
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Divya
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Hoshyar
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Hoshyar
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Divya
can man city win Liverpool ?
There are two coins on a table. When both are flipped, one coin land on heads eith probability 0.5 while the other lands on head with probability 0.6. A coin is randomly selected from the table and flipped. (a) what is probability it lands on heads? (b) given that it lands on tail, what is the Condi
0.5*0.5+0.5*0.6
Ravasz
It should be a Machine learning terms。
Mok
it is a term used in linear regression
Saurav
what are the differences between standard deviation and variancs?
Enhance
what is statistics
statistics is the collection and interpretation of data
Enhance
the science of summarization and description of numerical facts
Enhance
Is the estimation of probability
Zaini
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Haai
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Enhance
Haai how r u?
Enhance
maybe .... mathematics is the science of simplification and statistics is the interpretation of such values and its implications.
Miguel
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Haai