97.5th percentile point

Because of the central limit theorem, this number is used in the construction of approximate 95% confidence intervals.

[9] There is no single accepted name for this number; it is also commonly referred to as the "standard normal deviate", "normal score" or "Z score" for the 97.5 percentile point, the .975 point, or just its approximate value, 1.96.

[10] From the probability density function of the standard normal distribution, the exact value of z.975 is determined by Its square, about 3.84146, is the 95th percentile point of a chi-squared distribution with 1 degree of freedom, often used for testing 2×2 contingency tables.

The use of this number in applied statistics can be traced to the influence of Ronald Fisher's classic textbook, Statistical Methods for Research Workers, first published in 1925: "The value for which P = .05, or 1 in 20, is 1.96 or nearly 2; it is convenient to take this point as a limit in judging whether a deviation is to be considered significant or not.

[12] In 1970, the value truncated to 20 decimal places was calculated to be The commonly used approximate value of 1.96 is therefore accurate to better than one part in 50,000, which is more than adequate for applied work.