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Calculating probabilities for a normal distribution
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We can compare any normal distribution to the standard normal distribution by using the formula:
X = normal random variable µ = any value σ = any value Z = standard normal random variable µ = 0 σ = 1
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Example X is a normally distributed random variable with µ =33 and σ = 8. Find: P(X <20) X=20 µ =33 Step 1: Draw a diagram Step 2: Use GC
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Graphics Calculator P(X <20)= 0.0521 Stats Mode Dist = F5 Norm = F1
Ncd = normal distribution probability P(X <20)= Upper limit = 20 Lower limit = -∞ µ =33 σ = 8 X=20 µ =33
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Example X is a normally distributed random variable with µ =33 and σ = 8. Find: P(X<20) = P(Z< ) = P(Z < ) =P(Z < ) = 0.5 – = P(X<20) = P(Z< ) = P(Z < ) =P(Z < ) = 0.5 – = P(X<20) = P(Z< ) = P(Z < ) =P(Z < ) = 0.5 – = X=20 µ =33
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