AP Stats quiz 6.5-.7

Requirements for something to be a binomial

BINS → binary (can only be yes or no), independent trials, # of things is fixed, same probability of success

What does each part of the binomial formula mean?

P = probability of success (%), n = # of trials, x/k = # of successful trials

(P)^k

probability of success

(1-P)

probability of failure

N-k

Number of failures

nCk

number of ways to get successes

How to find P(x = k) with calculator

binomPDF (n,p,k)

How to find P(x < k) with calculator

binomCDF (n,p,k)

How to find mean of binomial

Mx = n(p) “after many trials, the average number of successes is (mean)”

How to find the standard deviation of binomial

√np (1-p) “the number of successes typically varies by (SD) from the mean of (m)”

How to find the probability when the equation is NOT a binomial setting

either use the 10% probability or multiply together every successful trial

10% conditional probability

n < (0.10)N, n = sample size, N = population size

How to model a binomial distribution

by using a normal distribution

How to know when something is able to be represented by a normal distribution?

Both equations (n x p) and n(1 - P) must be less than or equal to 10 for a normal distribution to be valid

Equation for binomial formula