The Standard Normal Distribution (HSC SSCE Mathematics Advanced): Flashcards

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The Standard Normal Distribution
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Random variable symbol for std normal dist

ZZ

PDF symbol for std normal dist

ϕ(z)\phi(z)

CDF symbol for std normal dist

Φ(z)\Phi(z)

Mean of std normal dist

μ=0\mu = 0

Standard deviation of std normal dist

σ=1\sigma = 1

Inflection points of std normal curve

z=1z = -1 and z=1z = 1

Value of Φ(0)\Phi(0)

0.50.5

% within 1 std dev (empirical rule)

Approximately 68%

% within 2 std devs (empirical rule)

Approximately 95%

% within 3 std devs (empirical rule)

Approximately 99.7%

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