The standard normal distribution

Answer

Standard Normal Distribution

A Standard normal distribution with a mean of zero and a standard deviation of one is known as the standard normal distribution. The standard normal distribution is centered at zero, and the standard deviation indicates how much a measurement deviates from the mean. The conventional normal distribution has 68 percent of observations within one standard deviation of the mean, 95 percent within two standard deviations, and 99.9% within three standard deviations of the mean.

The distribution is used to calculate normal probabilities by use of the standard normal tables which gives the area to the left of a given z score.

The link below provides the standard normal table:

https://www.math.arizona.edu/~rsims/ma464/standardnormaltable.pdf

Standard normal distribution example 

Notably, several data analysis follows a normal distribution. The following are the example of a normal distribution:

·       Size of items produced by a machine

·       Marks on a test

·       Errors in Measurements

·       Heights of students

·       Blood Pressure

A normal distribution of standardized values known as z-scores is known as the standard normal distribution. The standard deviation is used to calculate the z-score. The value 11 is three standard deviations above (or to the right of) the mean in a normal distribution with a mean of five and a standard deviation of two.

Here's how to figure it out:

$x=\mu +z\left(\delta \right)$

$x=5+3\left(2\right)$

$x=11$

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