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Subject:  Statistics

P(X ≤ 115) for IQ with μ = 100, σ = 15

Find the cumulative probability for a normal distribution modelling IQ scores.

Answer P(X ≤ 115) = 0.841345, P(X ≥ 115) = 0.158655

Solution

  1. Distribution X ~ N(μ = 100, σ = 15)
  2. Z-score z = (x − μ) / σ = 1
  3. P(X ≤ x) Φ(z) = 0.841345
  4. P(X ≥ x) 1 − Φ(z) = 0.158655

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