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Statistics — Third Secondary
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Curriculum
Statistics — Third Secondary
Unit 1: Correlation and Regression
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Correlation
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Correlation — Lesson quiz
6 questions
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Regression
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Regression — Lesson quiz
6 questions
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Unit 2: Advanced Statistical Measures
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Advanced Measures of Dispersion
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Advanced Measures of Dispersion — Lesson quiz
6 questions
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Unit 3: Probability
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Conditional Probability and Independent Events
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Conditional Probability and Independent Events — Lesson quiz
6 questions
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Unit 4: Random Variables
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Discrete Random Variables
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Discrete Random Variables — Lesson quiz
6 questions
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Expectation and Variance
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Expectation and Variance — Lesson quiz
6 questions
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Unit 5: The Normal Distribution
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The Normal Distribution and Its Applications
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The normal distribution and its properties
The standard normal distribution and the table of areas
Converting to the standard variable Z
Real-life applications and reversed problems
Worked examples
Common mistakes
Lesson summary
The Normal Distribution and Its Applications — Lesson quiz
6 questions
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Text lesson
The Normal Distribution and Its Applications
Statistics — Third Secondary
The Normal Distribution and Its Applications
Explanation
Converting to the standard variable Z
Converting to the standard variable Z
If the variable X follows a normal distribution with mean μ and standard deviation σ, we write X ~ N(μ, σ²).
We convert it to a standard variable using the formula:
Z = (X − μ) ÷ σ
Then P(X ≥ c) = P(Z ≥ (c − μ) ÷ σ), and we complete the solution from the table.
The value of Z is called the standard score (z-score).
It tells us how many standard deviations the value lies above or below the mean.
The Normal Distribution and Its Applications · 3 / 7
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