Chapter17 - Chapter 17 - Bernoulli Trials and the Binomial...

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1 Chapter 17 - Bernoulli Trials and the Binomial Distribution Read: Searching for Tiger (pg. 432–433); Independence (pg. 434-435); The Binomial Model (pg. 436-438); The Normal Model to the Rescue (pg. 439); Continuous Random Variables (pg. 441); What Can Go Wrong (443–444) Skip: Geometric Model (pg 433-434); Step-By-Step Example (pg 435-436); Why 10? (pg 440); Poisson Model (pg 441-443) The primary focus of this chapter is on calculating binomial probabilities. So, how do we know when the given scenario involves a binomial probability calculation? Any scenario that satisfied each of the following conditions is said to involve Bernoulli Trials : (See the bullets at the top of page 433) 1. Each trial has only two possible outcomes (success or failure) 2. There are a fixed number of observations/trials ( n ) 3. The probability of success ( p ) remains constant for each trial 4. The outcome of each trial is independent of the outcome of any previous trial The corresponding probability calculations are called binomial probabilities . Activity 1: According to the U.S. Department of Education, 57% of this year’s incoming college freshmen are female. Suppose a random sample of forty of this year’s freshmen is collected, and the gender of each is recorded. Note that there are only two possible outcomes for each, female or male. Also, assume we define a success as a freshman female and a failure as a freshman male. A. Consider that each randomly selected freshman is called a trial. How many trials ( n ) are being run in this study? B. What is the probability of success ( p ) for any trial? P(success) = p C. What is the probability of failure ( q ) for any trial? P(failure) = q Note: q = 1 – p because there are only two possible outcomes for each trial (a success or a failure) D. Are the outcomes of consecutive trials independent or dependent on each other? Note: Technically, the trials are not independent . Assuming we are sampling without replacement , the outcome of the first trial does affect the outcome of the second trial. If the outcome of the first trial was a success (female), there is one fewer successes (females) left in the remaining population for the next draw, causing the probability of success ( p ) to be lower than 0.57 for the second trial. However, because we are sampling from such a large population (all U.S. freshmen), this change in p is negligible. Rule of Thumb:
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This note was uploaded on 11/22/2010 for the course STA 2023 taught by Professor Ripol during the Spring '08 term at University of Florida.

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Chapter17 - Chapter 17 - Bernoulli Trials and the Binomial...

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