MAT-152 Written Assignment 06
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Chatham Charter High School *
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Course
152
Subject
Mathematics
Date
Apr 30, 2024
Type
docx
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4
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MAT-152 Written Assignment 6
Answer the following questions. You can either handwrite your solutions (e.g., by printing this
document and writing on paper or by using a program), or you can type your solutions below.
You do not need to show your work for this assignment.
(Prompt for #1 to #4) Consider the experiment of rolling two fair six-sided dice. Let x̄
be the
mean of the values shown on the dice. 1. Fill in the tables below for the possible values of the sample mean, x̄
Sample
x̄
1,1
1,2
1,3
1,4
1,5
1,6
Sample
x̄
4,1
4,2
4,3
4,4
4,5
4,6
Sample
x̄
2,1
2,2
2,3
2,4
2,5
2,6
Sample
x̄
5,1
5,2
5,3
5,4
5,5
5,6
Sample
x̄
3,1
3,2
3,3
3,4
3,5
3,6
Sample
x̄
6,1
6,2
6,3
6,4
6,5
6,6
2.
Using your tables from #1, construct the sampling distribution for in the table below.
x̄
You may or may not need every row, and you can add additional rows if needed. You
can write the probabilities as fractions or as decimals rounded to 4 decimal places.
x̄
P(
x̄)
3.
Using your sampling distribution from #2, calculate the mean of the sampling
distribution of the sample mean (i.e., the expected value of ). You can do this in your
x̄
calculator.
4.
Using your sampling distribution from #2, calculate the standard deviation of the
sampling distribution of the sample mean. You can do this in your calculator.
5.
Suppose that random samples of size n are taken from a population with mean µ and
standard deviation σ. Fill in the blanks in the following statement: If n is large, the sampling distribution of the sample mean, x
is approximately ________,
with mean _______ and standard deviation (standard error) _______.
6.
Suppose that random samples of size n are taken from a population with mean µ and
standard deviation σ. Fill in the blanks in the following statement: If n is large, the sampling distribution of the sum of the samples, Σx, is approximately
________, with mean _______ and standard deviation (standard error) _______.
7.
A geologist studying the movement of Earth’s crust at a particular location on
California’s San Andreas fault found many fractures in the local rock structure. In an
attempt to determine the mean angle of the breaks, she sampled n = 50 fractures and
found the sample mean and standard deviation to be 39.8° and 17.2° respectively.
Determine the point-estimate of the mean angle of the fractures and find the 95%
margin of error for that estimate.
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