Standard Normal Distri.
(Z~N(0,1))
Same, but with \(\mu = 0\) and \(\sigma = 1\)
For Y~N(\(\mu, \sigma^2)\)
\(
P(a < Y ≤ b)=Φ(\frac{b-\mu}{\sigma}) - Φ(\frac{a-\mu}{\sigma})
\)
Properties:
P(Z≥0) = P(Z≤0) = 0.5
P(Z≤x) = 1-P(Z>x)
P(Z≤ -x) = P(Z≥x)
-Z~N(0,1)
If Y ~ N \((\mu, \sigma^2), then X = \frac{Y-\mu}{\sigma}\)~N(0,1)
If X~N(0,1), then Y = aX+b ~ N(b,\(a^2\))