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# Statistics Ch 5.3 STAT 1070

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This 3 page Class Notes was uploaded by Alikhan Ladhani on Sunday February 28, 2016. The Class Notes belongs to STAT 1070 at Georgia State University taught by Professor Kemp in Spring 2016. Since its upload, it has received 42 views. For similar materials see Elementary Statistics in Statistics at Georgia State University.

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Date Created: 02/28/16

Math 1070 – Elementary Statistics on the texts: Elementary Statistics with Excel, Third Custom Edition for Math1070; Georgia State University and Elementary Statistics; Eleventh Edition. Mario F. Triola, and coordinating PowerPoint Slides. Chapter 5 – Discrete Probability Distributions 5-3 – Binomial Probability Distributions Definition A binomial probability distribution results from a procedure that meets all of the following requirements: 1. The procedure has a fixed number of trials. 2. The trials must be independent. (the outcome of any individual trial does not affect the probability in the other trials.) 3. Each trial must have all outcomes classified into two categories (commonly referred to as success and failure). 4. The probability of a success remains the same in all trials. Treating Dependent Events as Independent (For requirement #2 abovWhen selecting a sample without replacement, if calculations are cumbersome and if a sample size is no more than of the size of the population, treat the selections as being independent (instead of treating them, by definition, as being dependent). Notation for Binomial Probability Distributions and (success and failure) denote the two possible categories ofall outcomes. -denotes the fixed number of trials. -denotes a specific number of successes in trials,so can be any whole number between and inclusive. -denotes the probability of successin one of thtrials -denotes the probability of failure in one of the trials -denotes the probability of getting exactsuccesses among the trials. Example - Genetics: Consider the offspring of peas from parents both having the green/yellow combination of pod genes. Under these conditions the probability that the offspring has a green pod is or , i.e., . Assume five such offspring are obtained and let: Suppose we want to find the probability that exactly of the offspring peas have a green pod. a. How do we know that this procedure results in a binomial probability distribution? b. Identify the values of , , and . c. Find given, Formula 5-5: Excel =BINOM.DIST( , , , ) – “false” indicator of cumulative (exactly ) d. Find the probability that or fewer of the offspring peas have a green pod. Excel =BINOM.DIST( , , , ) – “true” indicator of cumulative ( or fewer) Example – McDonald’s Brand Recognition: The fast food chain McDonald’s has a brand name recognition of around the world (based on data from Retail Marketing Group). Assuming that we randomly select people, find the following: a. The probability that exactly of the people recognize McDonald’s. b. The probability that or fewer of the recognize McDonald’s.

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