Chapter 5.5（课件）- 《统计学基础（英文版）》同步教学（人民大学版）

Chapter Normal Probability Distributions 5 1 Copyright 2019, 2015, 2012, Pearson Education, Inc. 1 Larson/Farber 6th ed Chapter 1 Chapter Outline 1 Copyright 2019, 2015, 2012, Pearson Education, Inc. Section 5.5 Normal Approximations to Binomial Distributions 1 Copyright 2019, 2015, 2012, Pearson Education, Inc. Section 5.5 Objectives How to determine when the normal distribution can approximate the binomial distribution How to find the continuity correction How to use the normal distribution to approximate binomial probabilities 1 Copyright 2019, 2015, 2012, Pearson Education, Inc. Normal Approximation to a Binomial Normal Approximation to a Binomial Distribution If np  5 and nq  5, then the binomial random variable x is approximately normally distributed with mean μ = np standard deviation where n is the number of independent trials, p is the probability of success in a single trial, and q is the probability of failure in a single trial. 1 Copyright 2019, 2015, 2012, Pearson Education, Inc. 5 Normal Approximation to a Binomial Binomial distribution: p = 0.25, q =1 – 0.25, and n = 4, n = 10, n = 25 and n = 50. As n increases the histogram approaches a normal curve. 1 Copyright 2019, 2015, 2012, Pearson Education, Inc. 6 In a survey of 8- to 18-year-old heavy media users in the United States, 47% said they get fair or poor grades (C and below). You randomly select forty-five 8- to 18-year-old heavy media users in the United States and ask them whether they get fair or poor grades. (Source: Kaiser Family Foundation) Example: Approximating a Binomial Distribution Two binomial experiments are listed. Determine whether you can use a normal distribution to approximate the distribution of x, the number of people who reply yes. If you can, find the mean and standard deviation. If you cannot, explain why. 1 Copyright 2019, 2015, 2012, Pearson Education, Inc. 7 Example: Approximating a Binomial Distribution In a survey of 8- to 18-year-old light media users in the