Formulas Sheet

Mean: $\bar{x} = \frac{\sum x}{n}$

Variance: $s^2 = \frac{\sum(x - \bar{x})^2}{n-1}$

Std Dev: $s = \sqrt{s^2}$

Addition Rule: $P(A \cup B) = P(A) + P(B) - P(A \cap B)$

Conditional: $P(A|B) = \frac{P(A \cap B)}{P(B)}$

Binomial: $P(x) = \binom{n}{x} p^x (1-p)^{n-x}$

Confidence Interval (Mean): $\bar{x} \pm Z_{\alpha/2} \frac{\sigma}{\sqrt{n}}$

Z-Test Statistic: $Z = \frac{\bar{x} - \mu}{\sigma / \sqrt{n}}$

t-Test Statistic: $t = \frac{\bar{x} - \mu}{s / \sqrt{n}}$

Equation: $\hat{Y} = b_0 + b_1X$

Slope ($b_1$): $\frac{n\sum xy - (\sum x)(\sum y)}{n\sum x^2 - (\sum x)^2}$