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AP Statistics Review

AP Statistics Review. Probability(C14-C17 BVD) C17: Binomial and Geometric Probability Models. Many probability questions on AP exam fit a binomial model BINS B – Binary? Outcomes can be defined as success/fail.

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AP Statistics Review

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  1. AP Statistics Review Probability(C14-C17 BVD) C17: Binomial and Geometric Probability Models

  2. Many probability questions on AP exam fit a binomial model • BINS • B – Binary? Outcomes can be defined as success/fail. • I – Independent? Knowing result of one trial does not effect result of another trial • N – Number? Number of trials n fixed in advance • S – Success Same? Probability of success (p) is the same for each trial. Binomial Settings (Bernoulli Trials)

  3. X = number of successes in n trials • P(X=x) = nCx (px) (1-p)n-x • Mean µ = np • Standard deviation σ = sqrt(npq) • Notation: Binom(n,p) • Binompdf(n,p,X) • Binomcdf(n,p,X) – up to X successes • Complement rule (1- opposite) very handy • See page 331-332 for example BINS – check So now what?

  4. Many probability questions on AP exam fit a geometric model • BITS • B – Binary? Outcomes can be defined as success/fail. • I – Independent? Knowing result of one trial does not effect result of another trial • T– Trials? Asking how many trials until success • S – Success Same? Probability of success (p) is the same for each trial. BITS – Geometric Model

  5. X = number of trials until success • P(X=x) = (1-p)x-1p • Mean µ = 1/p • Standard deviation σ = sqrt(q/p2) • Notation: Geomet(n,p) • Geometpdf(p,X) • Geometcdf(p,X) – 1st success on or before trial x • Complement rule (1- opposite) very handy • See page 328 for example BITS – check So now what?

  6. Technically I in BINS or BITS is not met when in a sampling situation – when you draw from a finite population, the probability of the next event changes slightly (think of drawing Ace then Ace in a deck of cards) • However, if the sample is smaller than 10% of the population, the probabilities change slightly enough that they are almost as if they didn’t change at all. • So: 10% Condition – if sample is < 10% pop, we can still use Binomial/Geometric probability models and procedures Binomial/Geometric Probability Models when Sampling

  7. A Binomial model is approximately Normal if we expect at least 10 successes and 10 failures • (np and np ≥ 10) • If that is true, use N(µ,σ) instead of Binom(n,p,X) with Mean µ = np and Standard deviation σ = sqrt(npq) • C6 again! Success/Fail Condition

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