Week7_001 - STA 2023 c D.Wackerly Lecture 11 Thought I...

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STA 2023 c D.Wackerly - Lecture 11 147 Thought: “I personally think we developed language because of our deep need to complain” - Lily Tomlin Assignments : Today : pages 215–226 For tomorrow: Exercises 5.15, 5.16, 5.19, 5.20, For Wednesday: Read more on pages 198–208 For Thursday: Exercises 5.24, 5.25, 5.31, 5.36–37, 5.39–40, 95, 96, 98, 6.1, 6.3, 6.4
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STA 2023 c D.Wackerly - Lecture 11 148 For a continuous random variable, Probabilities of intervals are areas under curves: graph of f(x) a b P(a<X<b) The area under a curve above a single point is 0. area 0 Line has a For any single value , UNLIKE for discrete random variables, if is a continuous random variable,
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STA 2023 c D.Wackerly - Lecture 11 149 The Normal Distribution One very important continuous distribution. A random variable has a normal dist. with mean and std. dev. if its probability density is (p. 216) Recall: No need to know this formula. Formula traces out the “bell shaped curve”. Will write N As a shorthand for “ has a normal distribution with mean and std dev N MEANS “ has a normal distribution with mean and std dev
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STA 2023 c D.Wackerly - Lecture 11 150 The graph of the normal density is a symmetric, bell-shaped curve, centered at . The std dev, , measures the spread of the distribution. (See Figure 5.6, p. 216) 12 16 14 10 8 6 4 Two Normal Curves with Diff Means, Same Std Dev =1 σ =1 σ =8 μ μ =12 20 15 10 5 0 Two Normal Curves with Same Mean and Differnent Std Devs =1 σ =3 =10 σ μ μ =10
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STA 2023 c D.Wackerly - Lecture 11 151 The Standard Normal Distribution – p. 217 The r. v. is said to have a standard normal distribution if is normal with mean and std dev , i.e., Recall : -score : The -score gives the number of standard deviations is from . is larger than . is smaller than . . If is a standard normal random variable: . That is, the value of is already a -score.
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STA 2023 c D.Wackerly - Lecture 11 152 For any normal random variable, areas under normal curves between z-scores of and , for are given in Table IV, p. 809 .
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