Part A: Describe the properties of a normal distribution. Explain why there are an infinite number of normal distributions. How does a standard normal distribution differ from any from any other normal distribution, and how is it similar? Explain.

Part B: What is the transformation to standardize a normal random variable? Why do we standardize normal random variable to find normal areas? Explain.

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Solution:

Part A

The Normal Distribution is also referred to as the Gaussian distribution, especially in the field of physics. It is sometimes called the bell curve because of the way it looks.

The probability density function for the normal distribution is given by:

f(X)=frequency of random variable X
Population standard deviation.
Population mean
X=value of random variable.

Probabilities are obtained by getting the area under the curve inside of a particular interval.

The area under ...

Solution Summary

Solution explains the properties of normal disribution and standard normal distribution. It also explains how can a normal distribution be standardized. (Both the parts to given problem are answered in MS Word in about 350 words.)

... learned about normal distributions: a. Using your own words, tell me what the difference is between a normal distribution and a standard normal distribution. ...

... 40/10 = 4) <br> <br>P (74< Xbar < 81) = P [ (74-80)/4 < Z < (81-80)/4 ]= <br> <br>= P (-1.5 < Z < 0.25) = using standard normal distribution table <br> <br ...

Statistics Problem for standard normal distribution. ... Thanks. This solution is comprised of a detailed explanation of standard normal distribution or z score. ...

Standard Normal Distribution. ... Use Appendix Table for Normal Distribution to find area under Standard Normal Distribution curve to the left of z = 0.85 Answer. ...

... 3) Find the probability P(z < 0.37) using the standard normal distribution. ... 3) Find the probability P(z < 0.37) using the standard normal distribution. ...

... mean is 240 and the standard deviation is 50 ... Section 5.3: Normal Distributions: Finding Values. 4. Answer the questions about the specified normal distribution. ...

... That is, P (z > -a) = P (z < a) for all a > 0 Explanation: The standard normal distribution is symmetric about the mean and P (z < 0) = P (z > 0) = 0.5 Also P ...