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Statistics for Engineers October 31, 2007 Outline - The Normal Distribution and the Central Limit Theorem 1. The normal distribution. 2. The standard normal distribution. 3. Any normal distribution from standard normal distribution. 4. i.i.d. random variables X1 , . . . , Xn 5. The sum Y of i.i.d. random variables 6. The sum of independent normals is normal 7. The Central Limit Theorem 8. The distribution of the sample mean Homework 1. Read Section 3.5. 2. Do problems 3.26, 3.27 of the text. Useful R > pnorm(1,0,1) [1] 0.8413447 > dnorm(0,0,1) [1] 0.3989423 > rnorm(10,0,1) [1] 0.3046967 -0.4709662 -0.9043858 -1.0532504 [7] 0.9262808 0.2212721 -0.2212027 1.0105646 > qnorm(.75,0,1) [1] 0.6744898 > 0.7853981 0.9422723