The Binomial Distributions Section 8.1

Binomial Setting Each observation falls into one of two categories Fixed number, n, of observations n observations are all independent Probability of success, p, is the same for each observation

Binomial Distribution The distribution of the count X of successes in the binomial setting Parameters n and p Possible values of X are the whole numbers from 0 to n. X is B(n,p)

Abbreviations pdf-probability distribution function cdf-cumulative distribution function

Binomial Coefficient The number of ways of arranging k successes among n observations Formula on page 447

Binomial Probability Formula for calculating is on page 448

Mean and Standard Deviation of a Binomial Random Variable Mean is equal to the number of observations times the probability of success (np) Standard Deviation is the square root of the mean times 1 – p *These formulas only work for binomial distributions

Note: When n is large we can use normal probability calculations to approximate hard to calculate binomial probabilities

Rule of Thumb Use normal approximation when n and p satisfy the conditions that np is greater than or equal to 10 and n(1-p) is greater than or equal to 10

Practice Problems pg. 461 #8.27-8.34