H2 Math Statistics notes (Binomial to Correlation)

Volumes Cylinder: (pi)(r^2)(h) Cone: (⅓)(pi)(r^2)(h) Curved SA of cylinder: 2(pi)(r)(h) Curved SA of cone: 2(pi)(r)(slant height) Sine and Cosine rule Graph transformations: - f(x) → f(x + 2), means to translate 2 units in the negative x-direction. So the coordinate (1, 3) → (-1, 3) - The wording tells the truth - f(x) → f(x/2), means to scale by factor 2 parallel to the x-axis. So the coordinate (1, 3) → (2, 3) - Reflection is about the opposite axis (eg x replace by -x is reflection about the y-axis) IMPORTANT Binomial: - 100p% just means p - Questions with a lot of conditions (eg at least, at least), break up into two layers, find the probability for the inner layer and work from there - Binomial inception questions: Identify what your random variable in the question needs to represent: then that’s your focal point . Not any other measurement - Beware of these types of questions: “Find the probability that the 20th student she asks is the 5th student who has been infected by the disease before” → create a new random variable Y that denotes number of infected people out of 19 (because the last one must be reserved for the 5th person), find P (Y=4), then multiply by the

original binomial distribution probability that a person is infected out of the original binomial distribution n. Identifying is it normal or binomial distribution? - If the question you’re unsure of is the last part where the previous parts were all binomial distribution question, identify if this last part requires you to find “TOTAL” something (eg money, boxes), then solve using Normal Distribution! - If it asks you to find an individual characteristic like “a carton contains exactly 24 coupons” (where a carton has 12 family packs), then solve basic binomial distribution Question types X ~ B ( n, p) - Unknown p (solve with graph) - Unknown n (must be integer, use table) - Unknown X value (must be integer, use table) - Given mode, solve for unknown something: X=4 is mode, P(X=4) > P(X=5), P(X=4) > P(X=3) Normal Distribution: - Bell-shaped curve, horizontal axis is x - Mean in the middle, symmetrical about the mean, standard deviation sigma on both sides of the mean - Approximately 99.7% of the data falls within 3 standard deviations about the mean (important when they ask you to draw the curve and shade the area beyond a certain value, consider this reminder to not draw the shaded area too large) - normalc