AP Statistics - Unit 5: Probability Models (Chapter 16)

geometric and binomial probability models, binomial model :DDDDDDDDDDDDDDDDDDDDD

Bernoulli trials

only two possible outcomes, probability of success (p) is the same for every trial, trials are independent of each other

geometric probability model

about getting to the first success

P(X=x) = (1-p)^(x-1) * p

mean of a geometric probability model

1/p

standard deviation of a geometric probability model

[sqrt (1-p)] / p

probability that the first success is the nth trial

P(X=n) = (1-p)^(n-1) * p

geometric pdf (p, n)

probability that the first success within n trials

P(X=1) + P(X=2)...+ P(x=n)

geometric cdf (p, n)

binomial probability model

fixed number of trials

P(X=x) = (ⁿ_x) * p^x * (1 - p)^(nx)

n = number of trials

mean of a binomial probability model

np

standard deviation of a binomial probability model

sqrt (npq)

probability of x successes within n amount of trials

P(X=x) = (ⁿ_x) * p^x * (1 - p)^(nx)

binom cdf (n, p, x)

probability of fewer than x successes within n amount of trials

binom cdf (n, p, [x-1])

x is not included

probability of more than x successes within n amount of trials

1 - binom cdf (n, p, x)

x is not included

probability of at least x successes within n amount of trials

binom cdf (n, p, x)

x is included

probability of at most x successes within n amount of trials

1 - binom cdf (n, p, [x-1])

x is included

probability of between x₁ and x₂ successes in n amount of trials

binom cdf (n, p, x₂) - binom cdf (n, p, (x₁-1)

binomial model

use the normal model to predict

trials must be independent, success/failure condition

success/failure condition

there must be at least 10 successes and failure in order to use a normal model to predict the binomial model

np>= 10, nq >= 10