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 variableto 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 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.)