If the nonstandard normal distribution x ~ n (μ, σ 2), then a linear function (X-μ)/σ about x must obey the standard normal distribution N(0, 1).

For a concrete example, a quantity X is a nonstandard normal distribution with an expected value of 10 and a variance of 5 2 (that is, X ~ N (10, 5 2)); Then for the linear function of x, Y=(X- 10)/5, y is Y~N(0, 1) which obeys the standard normal distribution.

The standard normal distribution of extended data, also known as U distribution, is a normal distribution with 0 as the mean and 1 as the standard deviation, and is recorded as n (0, 1).

The distribution law of the area under the standard normal distribution curve is that the area under the curve is equal to 0.9500 in the range of-1.96 ~+ 1.96, and equal to 0.9900 in the range of -2.58 ~+2.58. Statisticians also made a statistical table (degree of freedom is ∞), which can be used to estimate the area under the curve in some special ranges of u 1 and u2.

References:

Baidu Encyclopedia-Standard Normal Distribution