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Probability Distributions
Published in Lawrence S. Aft, Fundamentals of Industrial Quality Control, 2018
When the values for normal probabilities were first tabulated, it was necessary to build a special table for each sample based on the sample average and standard deviation. Because of the great difficulty of the mathematics involved in the procedure the values were tabulated for a special case normal distribution. This is the case of a distribution with a mean of 0 and a standard deviation of 1. This distribution is known as the standard normal distribution. These values can be used for any normally distributed sample by converting the sample values to the standard normal distribution via the z transform. Once the z transform has been calculated, the values in the standard normal table can be employed to determine normal probabilities; z is essentially the number of standard deviations the value under analysis is from the mean.
Analyzing Variability
Published in Erick C. Jones, Supply Chain Engineering and Logistics Handbook, 2020
The Z value, hence, gives the number of standard deviations away from the mean and standard normal table that can be used to find the area under the curve, which gives the probability of occurrences. This book, as mentioned earlier, assumes that the reader is well aware of the concepts in probability.
A web-based application for generating statistical tables
Published in International Journal of Mathematical Education in Science and Technology, 2023
To illustrate, suppose the user selects the standard normal distribution with a shaded area to the left of the respective z-score, inputs six for the number of digits to round each decimal to, checks the box to drop leading zeros before decimals, and checks the box to include a table with common critical z-scores. The table generated by the app is split across two pages – one for negative z-scores and the other for positive z-scores – as is commonly done with the standard normal table. The resulting positive z-score page can be seen in Figure 3.