Chapter_13 - Chapter 13 Binomial Distributions BPS - 5th...

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BPS - 5th Ed. Chapter 13 1 Chapter 13 Binomial Distributions
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BPS - 5th Ed. Chapter 13 2 Fixed number n of observations The n 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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BPS - 5th Ed. Chapter 13 3 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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BPS - 5th Ed. Chapter 13 4 Let X = the count of successes in a binomial setting. 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 Binomial Distribution
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BPS - 5th Ed. Chapter 13 5 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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BPS - 5th Ed. Chapter 13 6 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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BPS - 5th Ed. Chapter 13 7 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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BPS - 5th Ed. Chapter 13
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This note was uploaded on 08/27/2011 for the course MA 116 taught by Professor Muntheralraban during the Summer '11 term at Montgomery CC.

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Chapter_13 - Chapter 13 Binomial Distributions BPS - 5th...

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