Statistics and Probability
Statistics and Probability
Algebra II statistics focuses on interpreting data and using probability models. For a normal distribution, convert to a z-score z = (x-mu)/sigma; positive z means above the mean. Use the empirical rule (68-95-99.7) for approximate areas and a standard normal table for precise areas, remembering that tables usually give area to the left. For probability, use P(A or B) = P(A)+P(B)-P(A and B); for independent events, P(A and B) = P(A)P(B). Conditional probability is P(A|B) = P(A and B)/P(B), with P(B) > 0. Two-way tables are ideal for these calculations; the denominator changes when the condition changes. Permutations count arrangements (order matters), combinations count groups (order does not), and binomial probability is C(n,k)p^k(1-p)^(n-k). Distinguish correlation from causation, and recognize that a margin of error describes sampling variability, not a guarantee about every individual.
Traps: using the wrong denominator in conditional probability, treating without replacement as independent, adding probabilities of overlapping events without subtracting the overlap, and using a z-score with the wrong sign.
Worked example: Scores are normal with mu = 500 and sigma = 100. Find P(X > 680). z = (680-500)/100 = 1.8. The table gives P(Z < 1.8) approximately 0.9641, so P(Z > 1.8) approximately 1-0.9641 = 0.0359.