Introduction to Probability and Statistics for Engineers and Scientists
204 Chapter 6: Distributions of Sampling Statistics 6.3The Central Limit Theorem In this section, we will consider one of the mo ...
6.3The Central Limit Theorem 205 ≈P{Z>3.51} whereZis a standard normal ≈.00023 Thus, there are only 2.3 chances out of 10,000 ...
206 Chapter 6: Distributions of Sampling Statistics or n≥ 117 then there is at least 1 chance in 10 that structural damage will ...
6.3The Central Limit Theorem 207 Enter the probabilities and number of random variables to be summed. The output gives the mass ...
208 Chapter 6: Distributions of Sampling Statistics Enter the probabilities and number of random variables to be summed. The out ...
6.3The Central Limit Theorem 209 Enter the probabilities and number of random variables to be summed. The output gives the mass ...
210 Chapter 6: Distributions of Sampling Statistics 0.30 0.25 0.20 0.15 0.10 0.05 0.0024 6 810 x (10, 0.7) 0.20 0.15 0.10 0.05 0 ...
6.3The Central Limit Theorem 211 Since a constant multiple of a normal random variable is also normal, it follows from the centr ...
212 Chapter 6: Distributions of Sampling Statistics EXAMPLE 6.3e An astronomer wants to measure the distance from her observator ...
6.4The Sample Variance 213 1.2 1.0 0.8 0.6 0.4 0.2 0.0 0.0 0.5 1.0 1.5 2.0 2.5 n = 1 n = 5 n = 10 FIGURE 6.4 Densities of the av ...
214 Chapter 6: Distributions of Sampling Statistics wherex= ∑n i= 1 xi/n. It follows from this identity that (n−1)S^2 = ∑n i= 1 ...
6.5Sampling Distributions from a Normal Population 215 6.5.1 Distribution of the Sample Mean Since the sum of independent normal ...
216 Chapter 6: Distributions of Sampling Statistics or, equivalently, ∑n i= 1 ( Xi−μ σ ) 2 = ∑n i= 1 (Xi−X)^2 σ^2 + [√ n(X−μ) σ ...
6.6Sampling from a Finite Population 217 The following corollary of Theorem 6.5.1 will be quite useful in the following chapters ...
218 Chapter 6: Distributions of Sampling Statistics Consider now the sum of theXi; that is, consider X=X 1 +X 2 +···+Xn Because ...
6.6Sampling from a Finite Population 219 is large in relation to the sample sizen, this change will be very slight. For instance ...
220 Chapter 6: Distributions of Sampling Statistics and SD(X)=SD(X)/n= √ p(1−p)/n EXAMPLE 6.6a Suppose that 45 percent of the po ...
Problems 221 SOLUTION If we letXibe the amount consumed by theith member of the sample, i=1,..., 25, then the desired probabilit ...
222 Chapter 6: Distributions of Sampling Statistics probability that (a) you are winning after 34 bets; (b) you are winning afte ...
Problems 223 (c) n=36; (d) n=64. 12.An instructor knows from past experience that student exam scores have mean 77 and standard ...
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