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##### Carefully define a standard normal distribution.

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**Question**

Carefully define a standard normal distribution. Why does a researcher want to go from a normal distribution to a standard normal distribution? Explain.;I need a comment (verify solution) in 25-150 words from the response given below from the question given above.;Simply put, the definition of a standard normal distribution is a normal distribution with a mean of 0 and a standard deviation of 1 as stated on page 201 of our text.;A researcher would want to go from a normal distribution to a standard normal distribution because the number of normal distributions is simply unlimited, with each having a different mean (mu), standard deviation, or both. Therefore, providing tables for the infinite number of normal distributions is quite impossible. A smart researcher can use the Standard Normal Distribution to determine the probabilities for all normal distributions. And this is how they can do it?;What is unique about the Standard Normal Distribution is that the mean is always equal to 0 and the standard deviation is always equal to 1, thus giving us a bell curve. Bell curves are easy to work with when solving problems as opposed to skewed curves. Any normal distribution can be converted to a Standard Normal Distribution by simply subtracting the mean from each observation and dividing this difference by the standard deviation. The results are called Z-scores.;Then we can take these Z-scores and determine the area underneath the bell curve to solve everyday probability riddles. Appendix B.1 quickly gives us the area underneath the bell curve depending on the value of the Z-score which greatly assists in determining probability.;From the 68-95-99.7 rule, we know that for a variable with the standard normal distribution, 68% of the observations fall between -1 and 1 (within 1 standard deviation of the mean of 0), 95% fall between -2 and 2 (within 2 standard deviations of the mean) and 99.7% fall between -3 and 3 (within 3 standard deviations of the mean). This makes calculating probabilities quick and easy.;For some reason, my illustrations would not stick on this post so I've pasted it to a Word document attachment so you could visually see what the 69-95-99.7 rule looks like.;References;Lind, Marchal, Wathen. Basic Statistics for Business & Economics, 7th Ed. McGraw-Hill Irwin. 2011: Page 201.;http://www.oswego.edu/~srp/stats/z.htm

Paper#26235 | Written in 18-Jul-2015

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