Determining Normal Probabilities (VCE SSCE Mathematical Methods): Flashcards

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Determining Normal Probabilities
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Normal CDF function

Calculates probability within a specified range

Inverse Normal function

Finds value (percentile) from a given probability

Standard normal distribution: μ\mu and σ\sigma

μ=0\mu = 0 and σ=1\sigma = 1

Percentile

Value below which a certain % of observations fall

Equal tail areas convention for symmetric intervals

Leave equal areas in each tail

Complement rule: Pr(Z>a)\text{Pr}(Z > a)

1Pr(Za)1 - \text{Pr}(Z \leq a)

Mirror symmetry: Pr(Z<a)\text{Pr}(Z < -a)

Equals Pr(Z>a)\text{Pr}(Z > a)

Symmetric interval: Pr(a<Z<a)\text{Pr}(-a < Z < a)

12Pr(Za)1 - 2\text{Pr}(Z \geq a)

Tail areas when central area is 95%

Each tail: 2.5% (0.025)

Use Inverse Normal when

You know probability and need to find the value

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