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Normal Distribution, Mean Difference, and Boxplot

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Could you show me how to solve the attached problem #1.
It's long, but it's still a basic statistics problem.

It asks four questions:
a) What is the sample distribution of "d"?

b) What assumptions made in a) are checked by the plots?

c) Calculate a 95% confidence interval for the difference, if 12 other points are collected.

d) Draw a boxplot.

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Solution Summary

This solution is provided in 520 words in an attached .doc file. It uses rules of a normal distribution to find standard deviation, uses calculations to solve for confidence interval, and includes a boxplot to satisfy the question.

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I've attached a Word document with the answers to your questions.

a) In order to answer this question, we make use of the following rule.

Let X1, X2, X3, ..., Xn be normally distributed random variables with mean and variance . Then

is also normally distributed with mean

and variance

In your question we have X1=speed and X2=roughness, which are normally distributed variables with mean 35 and 0.6 respectively and variance 4 and 0.0049 respectively. Since we're summing them just like in the above rule (D = 1* X1-3* X2), with c1=1 and c2=-3, then we conclude that D also follows a normal distribution, with mean

and variance

So the standard deviation is 2.0109.

b) The first plot (the one above) tells us basically the same as the next two. The ...

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