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In statistics, a standard normal table, also called the unit normal table or Z table, [1] is a mathematical table for the values of Φ, the cumulative distribution function of the normal distribution.
Each row of points is a sample from the same normal distribution. The colored lines are 50% confidence intervals for the mean, μ.At the center of each interval is the sample mean, marked with a diamond.
Diagram showing the cumulative distribution function for the normal distribution with mean (μ) 0 and variance (σ 2) 1. These numerical values "68%, 95%, 99.7%" come from the cumulative distribution function of the normal distribution. The prediction interval for any standard score z corresponds numerically to (1 − (1 − Φ μ,σ 2 (z)) · 2).
4.2 Confidence intervals. ... a normal distribution or Gaussian distribution is a type of continuous probability ... may be a value from a distribution table, ...
95% of the area under the normal distribution lies within 1.96 standard deviations away from the mean.. In probability and statistics, the 97.5th percentile point of the standard normal distribution is a number commonly used for statistical calculations.
Classically, a confidence distribution is defined by inverting the upper limits of a series of lower-sided confidence intervals. [15] [16] [page needed] In particular, For every α in (0, 1), let (−∞, ξ n (α)] be a 100α% lower-side confidence interval for θ, where ξ n (α) = ξ n (X n,α) is continuous and increasing in α for each sample X n.
In most such problems, if the standard deviation of the errors were known, a normal distribution would be used instead of the t distribution. Confidence intervals and hypothesis tests are two statistical procedures in which the quantiles of the sampling distribution of a particular statistic (e.g. the standard score) are required.
4.2.4 Confidence interval for ... A basic example is given by prediction intervals: For the normal distribution, ... contains a review and table of log-normal ...