4. Now imagine that you roll two dice, one red and one green. What are thepossible sample means that you could have? Complete the following table,entering the sample mean number of pips for each of the 36 possible outcomes.Some have been done for you.MAT 120 - Introduction to StatisticsACTIVITY #10: Central Limit Theorem.In this activity, we investigate the sampling distribution of the sample mean, X1345611. Imagine that you roll a single, fair, six-sided die once. Define the randomvariable X, to be the number of dots (pips) on the upward face, Complete theprobability distribution table for X.21.532.556P(x)15. Using the 36 sample means found in #4, complete the probability distributiontable for X, the mean number of pips on the faces when 2 dice are rolled.2345P(x)611.522. Sketch the probability histogram for X below. Let the x-axis be the OUTCOMEand let the y-axis be the PROBABILITY,2.533.544.555.56.Sketch the probability histogram for X below. Compare your results with thosein #2.3. Determine the mean and standard deviation for X. As a reminder, you determinethe mean of a discrete probability distribution using u =xP(x) and thestandard deviation is found most simply using the formulao =Ex' P(x) - u? (see.page 322). 9. If we were to repeat the process in # 1-6 for n=3 dice, there would be 216possible outcomes (why?); we would find the mean of the X distribution equalto 3.5 and the standard deviation equal to 1.71//3. The graph of the7. Compute the mean and standard deviation of the distribution in #5.distribution is shown below.Histogram of means, n=3 dice30252015108. Verify that your results in #3 and #7 agree with the information in the text onpage 401, "The mean of the sampling distribution of the sample mean is equal tothe mean of the underlying population, and the standard deviation of thesampling distribution of the sample mean is11.33 1.67 2 2.33 2.67 3 3.33 3.674 4.33 4.67 5 5.33 5.67 6%, regardless of the size of theExplain how the dice example illustrates the Central Limit Theorem, cited onpage 401 of the text:sample."The Central Limit TheoremRegardless of the shape of the underlying population, the sampling distribution ofx becomes approximately normal as the sample size, n, increases.

Name: 4. Now imagine that you roll two dice, one red and one green. What ar
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Description: 4. Now imagine that you roll two dice, one red and one green. What are thepossible sample means that you could have? Complete the following table,entering the sample mean number of pips for each of the 36 possible outcomes.Some have been done for yo

Note: Hi there! Thank you for posting the question. As your question has more than 3 parts, we have solved only the first three subparts for you. If you need any specific subpart to be answered, please re-submit the question by specifying the subpart number or name. (a). Define the probability distribution for the random variable X: Given that a fair six-sided die is rolled once. The random variable X represents the number of dots on the upward face. Since, the rolled die is fair, the probability of getting any numbers (1, 2, … , 6) is equal to 1/6. The probability distribution of the random variable X is obtained as given below: x P(x) 0 0 1 1/6 2 1/6 3 1/6 4 1/6 5 1/6 6 1/6(b). Sketch the probability histogram for X: Histogram for the data can be obtained using the EXCEL software. Software Procedure: The step-by-step procedure to obtain the histogram using EXCEL software is given below: Open an EXCEL file. Select the data of x in column A and the data of P(x) in column B. Go to Insert > Charts > All charts. Click on Column chart. In format data series change the gap width to Click OK. The generated output is given below:(c). Determine the mean and standard deviation for X: The mean µ is obtained as 3.5 from the calculation given below: The standard deviation σ is obtained as 1.7078 from the calculation given below:

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Statistics

- Imagine that you roll a single, fair, six-sided die once. Define the random variable X, to be the number of dots (pips) on the upward face. Complete the probability distribution table for X. P(x) 1 5 6.

- Imagine that you roll a single, fair, six-sided die once. Define the random variable X, to be the number of dots (pips) on the upward face. Complete the probability distribution table for X. P(x) 1 5 6.

MATLAB: An Introduction with Applications

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Concept explainers

Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.

Topic Video

Question

4. Now imagine that you roll two dice, one red and one green. What are the
possible sample means that you could have? Complete the following table,
entering the sample mean number of pips for each of the 36 possible outcomes.
Some have been done for you.
MAT 120 - Introduction to Statistics
ACTIVITY #10: Central Limit Theorem.
In this activity, we investigate the sampling distribution of the sample mean, X
1
3
4
5
6
1
1. Imagine that you roll a single, fair, six-sided die once. Define the random
variable X, to be the number of dots (pips) on the upward face, Complete the
probability distribution table for X.
2
1.5
3
2.5
5
6
P(x)
1
5. Using the 36 sample means found in #4, complete the probability distribution
table for X, the mean number of pips on the faces when 2 dice are rolled.
2
3
4
5
P(x)
6
1
1.5
2
2. Sketch the probability histogram for X below. Let the x-axis be the OUTCOME
and let the y-axis be the PROBABILITY,
2.5
3
3.5
4
4.5
5
5.5
6.
Sketch the probability histogram for X below. Compare your results with those
in #2.
3. Determine the mean and standard deviation for X. As a reminder, you determine
the mean of a discrete probability distribution using u =xP(x) and the
standard deviation is found most simply using the formula
o =Ex' P(x) - u? (see.page 322).

9. If we were to repeat the process in # 1-6 for n=3 dice, there would be 216
possible outcomes (why?); we would find the mean of the X distribution equal
to 3.5 and the standard deviation equal to 1.71//3. The graph of the
7. Compute the mean and standard deviation of the distribution in #5.
distribution is shown below.
Histogram of means, n=3 dice
30
25
20
15
10
8. Verify that your results in #3 and #7 agree with the information in the text on
page 401, "The mean of the sampling distribution of the sample mean is equal to
the mean of the underlying population, and the standard deviation of the
sampling distribution of the sample mean is
1
1.33 1.67 2 2.33 2.67 3 3.33 3.67
4 4.33 4.67 5 5.33 5.67 6
%, regardless of the size of the
Explain how the dice example illustrates the Central Limit Theorem, cited on
page 401 of the text:
sample."
The Central Limit Theorem
Regardless of the shape of the underlying population, the sampling distribution of
x becomes approximately normal as the sample size, n, increases.

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