**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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