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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.
The simplest case of a normal distribution is known as the standard normal distribution or unit normal distribution. This is a special case when μ = 0 {\textstyle \mu =0} and σ 2 = 1 {\textstyle \sigma ^{2}=1} , and it is described by this probability density function (or density): φ ( z ) = e − z 2 2 2 π . {\displaystyle \varphi (z ...
The standard definition of a reference range for a particular measurement is defined as the interval between which 95% of values of a reference population fall into, in such a way that 2.5% of the time a value will be less than the lower limit of this interval, and 2.5% of the time it will be larger than the upper limit of this interval, whatever the distribution of these values.
Comparison of the various grading methods in a normal distribution, including: standard deviations, cumulative percentages, percentile equivalents, z-scores, T-scores. In statistics, the standard score is the number of standard deviations by which the value of a raw score (i.e., an observed value or data point) is above or below the mean value of what is being observed or measured.
If a data distribution is approximately normal then about 68 percent of the data values are within one standard deviation of the mean (mathematically, μ ± σ, where μ is the arithmetic mean), about 95 percent are within two standard deviations (μ ± 2σ), and about 99.7 percent lie within three standard deviations (μ ± 3σ).
Skew normal distribution; Skewed generalized t distribution; Slash distribution; Split normal distribution; Standard normal deviate; Standard normal table; Student's t-distribution; Sum of normally distributed random variables
The skew normal distribution; Student's t-distribution, useful for estimating unknown means of Gaussian populations. The noncentral t-distribution; The skew t distribution; The Champernowne distribution; The type-1 Gumbel distribution; The Tracy–Widom distribution; The Voigt distribution, or Voigt profile, is the convolution of a normal ...
A graphical tool for assessing normality is the normal probability plot, a quantile-quantile plot (QQ plot) of the standardized data against the standard normal distribution. Here the correlation between the sample data and normal quantiles (a measure of the goodness of fit) measures how well the data are modeled by a normal distribution. For ...