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Concept
Standard normal table
Summary
In statistics, a standard normal table, also called the unit normal table or Z table, is a mathematical table for the values of Φ, the cumulative distribution function of the normal distribution. It is used to find the probability that a statistic is observed below, above, or between values on the standard normal distribution, and by extension, any normal distribution. Since probability tables cannot be printed for every normal distribution, as there are an infinite variety of normal distributions, it is common practice to convert a normal to a standard normal (known as a z-score) and then use the standard normal table to find probabilities.
Normal distributions are symmetrical, bell-shaped distributions that are useful in describing real-world data. The standard normal distribution, represented by Z, is the normal distribution having a mean of 0 and a standard deviation of 1.
Standard normal deviate
If X is a random variable from a normal distribution with mean μ and standard deviation σ, its Z-score may be calculated from X by subtracting μ and dividing by the standard deviation:
If is the mean of a sample of size n from some population in which the mean is μ and the standard deviation is σ, the standard error is \tfrac{\sigma}{\sqrt n}:
If is the total of a sample of size n from some population in which the mean is μ and the standard deviation is σ, the expected total is nμ and the standard error is \sigma \sqrt n:
Z tables are typically composed as follows:
The label for rows contains the integer part and the first decimal place of Z.
The label for columns contains the second decimal place of Z.
The values within the table are the probabilities corresponding to the table type. These probabilities are calculations of the area under the normal curve from the starting point (0 for cumulative from mean, negative infinity for cumulative and positive infinity for complementary cumulative) to Z.
Example: To find 0.69, one would look down the rows to find 0.6 and then across the columns to 0.09 which would yield a probability of 0.
Official source
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