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Course: Statistics — Third Secondary
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The Normal Distribution and Its Applications

Statistics — Third Secondary

The Normal Distribution and Its Applications

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

  1. Then P(X ≥ c) = P(Z ≥ (c − μ) ÷ σ), and we complete the solution from the table.
  2. The value of Z is called the standard score (z-score).
  3. It tells us how many standard deviations the value lies above or below the mean.
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