Chapter 4.2（课件）- 《统计学基础（英文版）》同步教学（人民大学版）

Chapter Discrete Probability Distributions 4 1 Copyright 2019, 2015, 2012, Pearson Education, Inc. 1 Larson/Farber 6th ed Chapter 1 Chapter Outline 4.1 Probability Distributions 4.2 Binomial Distributions 4.3 More Discrete Probability Distributions . 1 Copyright 2019, 2015, 2012, Pearson Education, Inc. Section 4.2 Binomial Distributions . 1 Copyright 2019, 2015, 2012, Pearson Education, Inc. Section 4.2 Objectives How to determine whether a probability experiment is a binomial experiment How to find binomial probabilities using the binomial probability formula How to find binomial probabilities using technology, formulas, and a binomial probability table How to construct and graph a binomial distribution How to find the mean, variance, and standard deviation of a binomial probability distribution . 1 Copyright 2019, 2015, 2012, Pearson Education, Inc. Binomial Experiments The experiment is repeated for a fixed number of trials, where each trial is independent of other trials. There are only two possible outcomes of interest for each trial. The outcomes can be classified as a success (S) or as a failure (F). The probability of a success, P(S), is the same for each trial. The random variable x counts the number of successful trials. . 1 Copyright 2019, 2015, 2012, Pearson Education, Inc. 5 Notation for Binomial Experiments Symbol Description n The number of times a trial is repeated p The probability of success in a single trial q The probability of failure in a single trial (q = 1 – p) x The random variable represents a count of the number of successes in n trials: x = 0, 1, 2, 3, … , n. . 1 Copyright 2019, 2015, 2012, Pearson Education, Inc. 6 Example: Identifying and Understanding Binomial Experiments Decide whether each experiment is a binomial experiment. If it is, specify the values of n, p, and q, and list the possible values of the random variable x. If it is not, explain why. A certain surgical procedure has an 85% chance of success. A doctor p