BUS310_L9_2.8.11 - Probability Lecture 9: Lecture 9:...

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Lecture 9: Probability
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Lecture 9: Outline 1. Review: Basic Probability Concepts Contingency tables and Venn Diagrams Simple event P(A), Complement P(A’), Joint event P(A and B), Union event P(A or B) Conditional Probability P(A I B) Independent events 2. Review: Properties of the Normal Distribution 3. NEW MATERIAL: Normal Distribution: Finding Probabilities and Values (Chapter 6) Finding probabilities: 1. Transforming normal data to the standardized normal scale (z-scale) 2. Using Table E.2 (Cumulative Standardized Normal Distribution) to find probabilities ‘Less than’ probabilities: Transform to z-value; look up probability directly (Table E.2) ‘Greater than’ probabilities: Transform to z-value; get probability by subtracting value (Table E.2) from 1 Probabilities between two values: Obtain 2 z-values, get probability by subtracting the 2 values obtained from Table E.2 Chapter6 (Table E.2: page 552), Handout Table E.2
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Why is the Normal Distribution Important? So far, we have only described the characteristics of samples (‘Descriptive Statistics’). If we only care about describing a specific sample, it does not matter if the distribution is normal or not. Many times, researchers want to do more than simply describing a sample: They want to know what the exact probability is of something occurring in their sample just due to chance If the average student in my sample consumes 2,000 calories per day, what are the chances (or probability) of having a student in the sample who consumes 1,000 calories per day? We rely on the characteristics of the Normal Distribution to calculate these probabilities They want to be able to make inferences about the population based on the data collected from the sample (Does the phenomenon observed in the sample represent an actual phenomenon in the population?) Hypothesize that in the population of men and women, there is no difference in the average number of calories consumed per day. Select a sample men and a sample of women, compare the average daily calorie consumption, find that men eat 200 calories more on average. Given the ‘Null Hypothesis’, what is the probability of finding a difference this large just by chance?
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Review Probabilities: Problem 4.10, 4.11, page 134 A yield improvement study at a semiconductor manufacturing facility provided defect data for a sample of 450 wafers . The following table presents a summary of the responses to two questions “Was a particle found on the die that produced the wafer?” “Is the wafer good or bad ?” a) Give an example of a simple event . If a wafer is selected at random, what is the probability that it was produced from a die with no particles? a)
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BUS310_L9_2.8.11 - Probability Lecture 9: Lecture 9:...

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