Binomial Distribution

Binomial Distribution - Stat 48 Lecture May 7th Binomial...

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Stat 48 Lecture May 7 th Binomial Distribution Dr Linda Penas Spring 2007 1 BINOMIAL DISTRIBUTION p. 93 An experiment often consists of repeated trials, each of which can result in one of two possible outcomes, either success or failure . EXAMPLE : Testing assembly line items, vaccines, etc. Binomial Experiment Characteristics of the Binomial Experiment : ¾ A trial has only two possible outcomes – “success” or “failure” ¾ Fixed number, n, of independent identical trials ¾ Probability of a success, p, remains constant from trial to trial ¾ q = (1-p) = is the probability of a failure “Success” vs “Failure” ¾ A manufacturing plant labels items as either “defective” or “acceptable” ¾ A firm bidding for a contract will either “get the contract” or “not get the contract” ¾ A marketing research firm receives survey responses of “yes I will buy” or “no I will not” ¾ New job applicants either “accept the offer” or “reject the offer” Example : A coin is tossed three times and the number of heads recorded. Is this a binomial experiment? SOLN : Yes since there are 3 independent repeated trials; success = {h}, failure = {t}, p remains constant (= ½ if balanced) EXAMPLE : Lots of 40 components each are called acceptable if they contain no more than 3 defectives. The procedure for sampling is to select 5 components, without replacement , at random and to reject the lot if a defective is found. Is this a binomial experiment? SOLN : No, since the trials are not independent – sampling without replacement trials cannot be independent Let X = the number of successes in a binomial experiment. Then X is a binomial r.v. and has the following distribution.

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