Chapter 5.2（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 5.2 Normal Distributions: Finding Probabilities 1 Copyright 2019, 2015, 2012, Pearson Education, Inc. Section 5.1 Objectives How to find probabilities for normally distributed variables using a table and using technology 1 Copyright 2019, 2015, 2012, Pearson Education, Inc. 4 Probability and Normal Distributions . If a random variable x is normally distributed, you can find the probability that x will fall in a given interval by calculating the area under the normal curve for that interval. μ = 500 σ = 100 600 μ = 500 x P(x < 600) = Area 1 Copyright 2019, 2015, 2012, Pearson Education, Inc. Probability and Normal Distributions . Consider a normal curve with  = 500 and  = 100 (upper right). The value of x one standard deviation above the mean is  +  = 500 + 100 = 600. Now consider the standard normal curve (lower right). The value of z one standard deviation above the mean is  +  = 0 + 1 = 1. The z-score of 1 corresponds to an x-value of 600, and areas are not changed with a transformation to a standard normal curve, the shaded areas at the right are equal. 1 Copyright 2019, 2015, 2012, Pearson Education, Inc. Example: Finding Probabilities for Normal Distributions . A national study found that college students with jobs worked an average of 22 hours per week. The standard deviation is 9 hours. A college student with a job is selected at random. Find the probability that the student works for less than 4 hours per week. Assume that the lengths of time college students work are normally distributed and are represented by the variable x. (Adapted from Sallie Mae/Ipsos Public Affairs) 1 Copyright 2019, 2015, 2012, Pearson Education, Inc. Solution The z-score that corresponds to 4 hours is z = = = 2. The Standard Normal Table shows that