When a random variable X following N(μ, σ²) is transformed as
Z = (X − μ)/σ, Z follows the standard normal distribution N(0, 1).
Probabilities can be read from a standard normal distribution table (or the table at the end of the book).
Example ① If height follows N(170, 25), find the Z-score for a height of 175 cm.
Solution:σ=5、Z = (175−170)/5 = 1.0
Solution:σ=5、Z = (175−170)/5 = 1.0
Key Point
- Z = (value − mean)/standard deviation
- The normal distribution table can be used with Z
Practice Problems
- For N(60, 16), find the Z-score when X=68.
Solutions and Explanations
- Solution:Z=2 (σ=4, (68−60)/4=2)