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
Lesson summary
Lesson summary
- The normal distribution is continuous and symmetric about the mean, and the total area under its curve equals 1.
- The standard normal variable Z has mean 0 and standard deviation 1.
- Conversion Z = (X − μ) ÷ σ, then the table of areas between 0 and z is used.
- P(Z ≥ a) = 0.5 − P(0 ≤ Z ≤ a), and P(−a ≤ Z ≤ a) = 2 P(0 ≤ Z ≤ a).
- To find a value whose probability is known, the steps are reversed using X = μ + zσ.
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