Example ① The lengths of screws from a factory follow N(20, 0.04) (mm). What is the probability that 19.8 ≦ X ≦ 20.2?
Solution:σ=0.2. The endpoints 19.8 and 20.2 are μ±σ.
Approximately 68%
Solution:σ=0.2. The endpoints 19.8 and 20.2 are μ±σ.
Approximately 68%
Key Point
- Make quick judgments using the idea of “mean ± σ, 2σ, or 3σ”
Practice Problems
- For N(100, 100), estimate the probability that X ≧ 130.
Solutions and Explanations
- Solution:approximately 0.15%
σ=10、Z=3、P(Z≧3)≈0.0013.