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1.96 is the approximate value of the 97.5 percentile point of the normal distribution used in probability and statistics. 95% of the area under a normal curve lies within roughly 1.96 standard deviations of the mean, and due to the central limit theorem, this number is therefore used in the construction of approximate 95% confidence intervals. Its ubiquity is due to the arbitrary but common convention of using confidence intervals with 95% coverage rather than other coverages (such as 90% or 99%).〔 〕〔 〕〔 〕 This convention seems particularly common in medical statistics,〔 〕〔 〕〔 〕 but is also common in other areas of application, such as earth sciences,〔 〕 social sciences and business research. 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, or .975 point. If ''X'' has a standard normal distribution, i.e. ''X'' ~ N(0,1), : : and as the normal distribution is symmetric, : One notation for this number is ''z''.025.〔 〕 From the probability density function of the normal distribution, the exact value of ''z''.025 is determined by : == History == 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:
In Table 1 of the same work, he gave the more precise value 1.959964.〔 , (Table 1 )〕 In 1970, the value truncated to 20 decimal places was calculated to be :1.95996 39845 40054 23552...〔 〕 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. == Software functions == The inverse of the standard normal CDF can be used to compute the value. The following is a table of function calls that return 1.96 in some commonly used applications: 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「1.96」の詳細全文を読む スポンサード リンク
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