Chapter 5.1（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 5.1 Introduction to Normal Distributions and the Standard Normal Distributions 1 Copyright 2019, 2015, 2012, Pearson Education, Inc. Section 5.1 Objectives How to interpret graphs of normal probability distributions How to find areas under the standard normal curve 1 Copyright 2019, 2015, 2012, Pearson Education, Inc. 4 Properties of a Normal Distribution Continuous random variable Has an infinite number of possible values that can be represented by an interval on the number line. Continuous probability distribution The probability distribution of a continuous random variable. . Hours spent studying in a day 0 6 3 9 15 12 18 24 21 The time spent studying can be any number between 0 and 24. 1 Copyright 2019, 2015, 2012, Pearson Education, Inc. Properties of a Normal Distribution . Normal distribution A continuous probability distribution for a random variable, x. The most important continuous probability distribution in statistics. The graph of a normal distribution is called the normal curve. x 1 Copyright 2019, 2015, 2012, Pearson Education, Inc. Properties of a Normal Distribution . The mean, median, and mode are equal. The normal curve is bell-shaped and is symmetric about the mean. The total area under the normal curve is equal to one. The normal curve approaches, but never touches the x-axis as it extends farther and farther away from the mean. x Total area = 1 μ 1 Copyright 2019, 2015, 2012, Pearson Education, Inc. Properties of a Normal Distribution . Between μ – σ and μ + σ (in the center of the curve), the graph curves downward. The graph curves upward to the left of μ – σ and to the right of μ + σ. The points at which the curve changes from curving upward to curving downward are called the inflection points. Inflection points μ  3σ μ + σ μ 