Question

What is a standard normal distribution? Give details explaination.

Answer 1

There are an infinite number of normal distributions. Although every normal distribution has a bell-shaped curve, some normal distributions have a curve that is tall and narrow; while others have a curve that is short and wide.

 

The exact shape of a normal distribution is determined by its mean and its standard deviation. The standard normal distribution is the normal distribution that has a mean of zero and a standard deviation of one.

 

The normal random variable of a standard normal distribution is called a standard score or a z-score. The normal random variable X from any normal distribution can be transformed into a z-score from a standard normal distribution via the following equation:

 

z = (X - μ) / σ

 

where X is a normal random variable, μ is the mean, and σ is the standard deviation.

 

Because any normal random variable can be "transformed" into a z-score, the standard normal distribution provides a useful frame of reference. In fact, it is the normal distribution that generally appears in the appendix of statistics textbooks

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