Chapter 5.3（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 5.3 Normal Distributions: Finding Values 1 Copyright 2019, 2015, 2012, Pearson Education, Inc. Section 5.3 Objectives How to find a z-score given the area under the normal curve How to transform a z-score to an x-value How to find a specific data value of a normal distribution given the probability 1 Copyright 2019, 2015, 2012, Pearson Education, Inc. Finding values Given a Probability In a previous section we were given a normally distributed random variable x and we were asked to find a probability. In this section, we will be given a probability and we will be asked to find the value of the random variable x. x z probability 1 Copyright 2019, 2015, 2012, Pearson Education, Inc. 5 Example: Finding a z-Score Given an Area Find the z-score that corresponds to a cumulative area of 0.3632. Solution: 1 Copyright 2019, 2015, 2012, Pearson Education, Inc. 6 Solution: Finding a z-Score Given an Area Locate 0.3632 in the body of the Standard Normal Table. The values at the beginning of the corresponding row and at the top of the column give the z-score. The z-score is – 0.35. 1 Copyright 2019, 2015, 2012, Pearson Education, Inc. 7 Example: Finding a z-Score Given an Area Find the z-score that has 10.75% of the distribution’s area to its right. Solution: Because the area to the right is 0.1075, the cumulative area is 1 – 0.1075 = 0.8925. 1 Copyright 2019, 2015, 2012, Pearson Education, Inc. 8 Solution: Finding a z-Score Given an Area Locate 0.8925 in the body of the Standard Normal Table. The values at the beginning of the corresponding row and at the top of the column give the z-score. The z-score is 1.24. 1 Copyright 2019, 2015, 2012, Pearson Education, Inc. 9 Example: Finding a z-Score Given a Percentile Find the z-score that corresponds to each percentile.