# Example 2 in the pepsi challenge a random sample of

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Example 2: In the “Pepsi Challenge” a random sample of 20 subjects are asked to try two unmarked cups of pop (Pepsi and Coke) and choose which one they prefer. If preference is based solely on chance what is the probability that: a) 6 will prefer Pepsi? b) 12 will prefer Coke? c) at least 15 will prefer Pepsi? d) at most 8 will prefer Coke? Example 3: A certain medical test is known to detect 90% of the people who are afflicted with disease Y. If 15 people with the disease are administered the test what is the probability that the test will show that: a) all 15 have the disease? b) at least 13 people have the disease? c) 8 have the disease? Homework: Day 1: pg 516, 8.1-8.6; pg 519-20, 8.7, 8.8, 8.12, pg 524, 8.14

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Chapter 8: The Binomial and Geometric Distributions Example 4: Find the mean and standard deviation of a binomial distribution with n = 10 and p = 0.1 Example 5: Sample surveys show that fewer people enjoy shopping than in the past. A survey asked a nationwide random sample of 2500 adults if shopping was often frustrating and time-consuming. Assume that 60% of all US adults would agree if asked the same question, what is the probability that 1520 or more of the sample would agree? Example 6: Each entry in a table of random digits like Table B in our book has a probability of 0.1 of being a zero. a) Find probability of find exactly 4 zeros in a line 40 digits long. b) What is the probability that a group of five digits from the table will contain at least 1 zero? Example 7: A university claims that 80% of its basketball players get their degree. An investigation examines the fates of a random sample of 20 players who entered the program over a period of several years. Of these players, 10 graduated and 10 are no longer in school. If the university's claim is true, what is the probability that exactly 10 out of 20 graduate? Can you conclude anything about the university's claim? Homework: Day 2: pg 529, pg 535 – 38, 8.27, 8.29, 8.30, 8.32, 8.34, 8.35
Chapter 8: The Binomial and Geometric Distributions Section 8.2: The Geometric Distributions Knowledge Objectives: Students will: Describe what is meant by a geometric setting . Construction Objectives: Students will be able to: Given the probability of success, p , calculate the probability of getting the first success on the n th trial. Calculate the mean (expected value) and the variance of a geometric random variable. Calculate the probability that it takes more than n trials to see the first success for a geometric random variable. Use simulation to solve geometric probability problems. Vocabulary: Geometric Setting – random variable meets geometric conditions Trial – each repetition of an experiment Success – one assigned result of a geometric experiment Failure – the other result of a geometric experiment PDF – probability distribution function; assigns a probability to each value of X CDF – cumulative (probability) distribution function; assigns the sum of probabilities less than or equal to X Key Concepts: Geometric Probability Criteria An experiment is said to be a geometric experiment provided: 1. Each repetition is called a trial.

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