Chapter 13 - STAT 2053 Elementary Statistics Chapter 13...

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STAT 2053 – Elementary Statistics Chapter 13 – Binomial Distributions 1
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Chapter 13 Example : Suppose you take an exam that consists of 10 multiple choice questions, each with 4 possible answers. You haven’t studied, so you randomly guess on all 10 questions. How many are you going to get right? (We’ll answer this later) 2
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Chapter 13 Often, in certain situations where we repeat the same trial over and over, we want to count how many trials produce an outcome we consider “successful.” In this case, we need to produce a probability model for the count of successful outcomes. 3
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Chapter 13 4 Fixed number n of observations All n of our observations are independent Each observation falls into one of just two categories may be labeled “success” and “failure” The probability of success, p , is the same for each observation Binomial Setting
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Chapter 13 5 In a shipment of 100 televisions, how many are defective? counting the number of “successes” (defective televisions) out of 100 A new procedure for treating breast cancer is tried on 25 patients; how many patients are cured? counting the number of “successes” (cured patients) out of 25 Binomial Setting Examples
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Chapter 13 6 Let X = the count of successes in a binomial setting. If all 4 properties of the Binomial setting hold, then we say the distribution of X is the binomial distribution with parameters n and p . n is the number of observations p is the probability of a success on any one observation X takes on whole values between 0 and n Denoted: X ~ BIN( n , p ) Binomial Distribution
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Chapter 13 7 not all counts have binomial distributions trials (observations) must be independent the probability of success, p , must be the same for each observation if the population size is MUCH larger than the sample size n , then even when the observations are not independent and p changes from one observation to the next, the change in p may be so small that the count of successes ( X ) has approximately the binomial distribution Binomial Distribution
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Chapter 13 8 Case Study Inspecting Switches An engineer selects a random sample of 10 switches from a shipment of 10,000 switches. Unknown to the engineer, 10% of the switches in the full shipment are bad. The engineer counts the number X of bad switches in the sample.
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Chapter 13 9 Case Study Inspecting Switches X (the number of bad switches) is not quite binomial Removing one switch changes the proportion of bad switches remaining in the shipment (selections are not independent ) However, removing one switch from a shipment of 10,000 changes the makeup of the remaining 9,999 very little the distribution of X is very close to the binomial distribution with n =10 and p =0.1
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Binomial Distribution Example : Find the distribution of X for the
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This note was uploaded on 09/23/2011 for the course STAT 2053 taught by Professor Staff during the Fall '08 term at Oklahoma State.

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Chapter 13 - STAT 2053 Elementary Statistics Chapter 13...

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