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.

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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 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
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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.
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  • 1.96
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