Empirical Rule by itself insufficient

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QUESTION

 

Why are standard z values so important? Is it true that z values have no units of measurement? Why would this be desirable for comparing data sets with different units of measurement? How can we assess differences in quality or performance by sampling comparing z values under a standard normal curve?

 

 

 

Second Question:

Explain the relationship between area and probability.

Third Question:

 

 

 

Why is the Empirical Rule by itself insufficient?

Fourth Question:

 

What is Normal?

Give some examples of variables that would have an approximately normal distribution.

Fifth Question:

a) What is a control chart and what is it used for?

b) What are the steps for constructing a Control Chart?

c) Explain the out of control signals?

 

Fourth Question: Sampling Distributions

To understand sampling distributions, consider the following:

Suppose the numbers 1, 2, 3, 4, and 5 are placed on slips of paper and put in a hat. Suppose we wish to draw two at a time, with replacement. What are the possible samples of two numbers? {1, 5} is not the same as {5,1}. Once all the samples have been written down (this is easiest if you make a matrix with 1,2 3, 4 and 5 as the labels of the rows and also the labels of the columns) determine the mean of each sample. Calculate the probabilities associated with each mean and then form a histogram with the means along the horizontal axis and the probabilities along the vertical axis. What is the shape of this histogram?

 

This is a very small sample. What does the Central Limit Theorem tell us about the ideal sample size? What are the hypotheses of the Central Limit Theorem?

 

What is the underlying distribution of just x when drawing the numbers 1, 2, 3, 4 and 5 where x is the number drawn? What would the histogram of just x look like?

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