normal distribution

denoted by N(µ, σ2). It has mean µ and variance σ2. The distribution is widely used in statistics because many experiments produce data that are approximately normally distributed; the sum of random variables from non-normal distributions is approximately normally distributed (see Central Limit Theorem), and it is the limiting distribution of distributions such as the binomial, Poisson, and chi-squared distributions. It is called the standard normal distribution when µ =  0 and σ2 = 1.

Density function of standard normal

If X has the distribution N(µ, σ2) and Z = (X−µ)/σ, then Z has the distribution N(0,1). The diagram shows the graph of the probability density function of N(0,1).

The table gives, for each value z, the percentage of observations which exceed z, for the standard normal distribution N(0,1). Thus the values are to be used for one-tailed tests. Interpolation may be used for values of z not included.

P(Z≥z) as percentages

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