09_08ans - STAT 400 Fall 2011 Examples for Binomial...

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STAT 400 Examples for 09/08/2011 Fall 2011 Binomial Distribution : 1. The number of trials, n , is fixed. 2. Each trial has two possible outcomes: “success” and “failure”. 3. The probability of “success”, p , is the same from trial to trial. 4. The trials are independent. 5. X = number of "successes" in n independent trials. Then ( ) ( ) k n k k n k p p k C n p p k n k - - = - - = = 1 1 P ) ( X , where k = 0, 1, … , n . E ( X ) = n p Var ( X ) = n p ( 1 p ) SD ( X ) = ( ) p p n - 1 1. Bart Simpson takes a multiple choice exam in his Statistics 101 class. The exam has 15 questions, each has 5 possible answers, only one of which is correct. Bart did not study for the exam, so he guesses independently on every question. Let X denote the number of questions that Bart gets right. a) Is it appropriate to use Binomial model for this problem? Yes . Binomial, n = 15, p = 1 / 5 = 0.20. b) What is the expected number of questions that Bart would get right? E ( X ) = n p = 15 0.20 = 3 .
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