Math 137 Unit 6 & 7 Formulas:
Counting Principles
a. Basic counting: l x m x n x ……… different ways possible (or different combinations)
𝑛!
b. If order matters and the number of objects is too large you can use the following instead: (𝑛−𝑟)!
(Ex. Choosing president and vice president of a club)
𝑛!
c. If order does not matter than you get less combinations. Use this: (𝑛−𝑟)!𝑟!
(Ex. Choosing two committee members of a club)
d. 0! = 1
Probability Distributions
x
P(x)
Expected value:
E(x) = mean = ∑ 𝑥𝑖 ∙ 𝑃(𝑥𝑖 )
μ = mean = ∑ 𝑥𝑖 ∙ 𝑃(𝑥𝑖 )
σ = standard deviation = √∑(𝑥𝑖 − 𝜇)2 ∙ 𝑃(𝑥𝑖 )
Normal Distribution
Empirical rule: 1 standard deviation captures 68% of the population
2 standard deviations capture 95% of the population
3 standard deviations capture 99.7% of the population (almost all)
Within ±1 SD: typical
Beyond ±2 SD: unusual
Beyond ±3 SD: extremely unusual
Z score =
𝑥− 𝜇
𝜎