A standard normal distribution is a normal distribution with zero mean () and unit variance (), given by the probability density function and distribution function
(1)
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(2)
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over the domain .
It has mean, variance, skewness, and kurtosis excess given by
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(4)
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(5)
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The first quartile of the standard normal distribution occurs when , which is
(7)
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(8)
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(OEIS A092678; Kenney and Keeping 1962, p. 134), where is the inverse erf function. The absolute value of this is known as the probable error.