TheNormalDistribution

Under the curve fx by the area p a x b a b x

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Unformatted text preview: the curve f(X) by the area P (a ≤ X ≤ b) a b X Probability as Probability Area Under the Curve Area The total area under the curve is 1.0 or 100%, and the curve is symmetric, so 50% is above the mean, 50% is below f(X) 0.5 0.5 μ P(−∞ < X < ∞ ) = 1.0 X General Procedure for Finding Probabilities Finding To find P(a < X < b) when X is distributed normally: Step 1: Draw the normal curve for the problem in terms of X terms Step 2: Translate X-values to Z-values Step 3: Use the Standardized Normal Table Solving for Probabilities Solving Suppose X is normal with mean 8.0 and Suppose standard deviation 5.0 standard Find the probability that someone will Find score above 8.6. score X 8.0 8.6 Finding the Raw Score for a Finding Known Probability Known Steps to find the raw score or X value raw for a known probability: for 1. Find the Z value for the known 1. probability probability 2. Convert to X units using the formula: X = μ + Zσ...
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