Curriculum
Statistics — Third Secondary
Unit 1: Correlation and Regression
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Unit 2: Advanced Statistical Measures
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Unit 3: Probability
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Unit 4: Random Variables
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Unit 5: The Normal Distribution
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Text lesson
The Normal Distribution and Its Applications
The Normal Distribution and Its Applications
The standard normal distribution and the table of areas
The standard normal distribution and the table of areas
- The standard normal distribution is the normal distribution with mean μ = 0 and standard deviation σ = 1.
- Its variable is denoted by Z.
- To find probabilities we use a table that gives the area between 0 and z, that is P(0 ≤ Z ≤ z).
- Some of the most important values of this table are:
| z | 0.5 | 1 | 1.5 | 2 | 2.5 |
|---|---|---|---|---|---|
| P(0 ≤ Z ≤ z) | 0.1915 | 0.3413 | 0.4332 | 0.4772 | 0.4938 |
- To find any probability we use the following rules
- where a is a positive number:
- P(0 ≤ Z ≤ a) is read directly from the table.
- P(Z ≥ a) = 0.5 − P(0 ≤ Z ≤ a), and P(Z ≤ a) = 0.5 + P(0 ≤ Z ≤ a).
- P(Z ≤ −a) = P(Z ≥ a), because the curve is symmetric.
- P(−a ≤ Z ≤ a) = 2 × P(0 ≤ Z ≤ a).
- It is advisable to sketch the bell curve and shade the required area before any calculation, so that you know whether to add 0.5 or subtract from it.
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