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Applied Mathematics · Ch 6 — Probability Distribution

Z-Score of Normal Distribution

6.7.2

Z-Score of Normal Distribution

A normal distribution with mean μ=0\mu = 0 and standard deviation σ=1\sigma = 1 is called the standard normal distribution, and the variable following it is called a standard normal variate; the distribution is also referred to as the Z-distribution.

Every normal variate, regardless of its own mean and standard deviation, can be converted into a standard normal variate. This is done by computing the Z-score (or standard score) of each data value — a transformation that puts values from different normal distributions onto the same scale, making them directly comparable.

Z=x−μσZ = \dfrac{x - \mu}{\sigma} …

Figure 4.7.2The area under the standard normal curve to the left of a z-score gives the cumulative probability P(Z ≤ z)
Fig. 4.7.2 — The area under the standard normal curve to the left of a z-score gives the cumulative probability P(Z ≤ z)

Drawn by us to help you understand the concept clearly, and verified to make sure it's accurate. For exams, practice from your NCERT textbook's own diagram.

The shaded area to the left of z under the standard normal curve equals the cumulative prob …