Summary of formulas

Normal probability distribution

$X$ ~ $N(\mu ,\sigma )$

$\mu$ = the mean $\sigma$ = the standard deviation

Standard normal probability distribution

$Z$ ~ $N(0,1)$

$z$ = a standardized value (z-score)

mean = 0 $$ standard deviation = 1

Finding the kth percentile

To find the kth percentile when the z-score is known: $k=\mu +\left(z\right)\sigma$

Z-score

$z=\frac{x-\mu }{\sigma }$

Finding the area to the left

The area to the left: $P(X< x)$

Finding the area to the right

The area to the right: $P(X> x)=1-P(X< x)$