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In this case, because the mean is zero and the standard deviation is 1, the Z value is the number of standard deviation units away from the mean, and the area is the probability of observing a value less than that particular Z value.
The standard normal distribution (z distribution) is a normal distribution with a mean of 0 and a standard deviation of 1. Any point (x) from a normal distribution can be converted to the standard normal distribution (z) with the formula z = (x-mean) / standard deviation.
The standard normal distribution table is a compilation of areas from the standard normal distribution, more commonly known as a bell curve, which provides the area of the region located under the bell curve and to the left of a given z-score to represent probabilities of occurrence in a given population.
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z = (x \u2013 \u03bc) / \u03c3 For example, let's say you have a test score of 190. The test has a mean (\u03bc) of 150 and a standard deviation (\u03c3) of 25. Assuming a normal distribution, your z score would be: z = (x \u2013 \u03bc) / \u03c3
While data points are referred to as x in a normal distribution, they are called z or z-scores in the z-distribution. A z-score is a standard score that tells you how many standard deviations away from the mean an individual value (x) lies: A positive z-score means that your x-value is greater than the mean.
To standardize a value from a normal distribution, convert the individual value into a z-score: Subtract the mean from your individual value. Divide the difference by the standard deviation.
To use the z-score table, start on the left side of the table go down to 1.0 and now at the top of the table, go to 0.00 (this corresponds to the value of 1.0 + . 00 = 1.00). The value in the table is . 8413 which is the probability.

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