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Let X1, X2, X100 represent the times necessary to perform 100 successive repair tasks at a certain service facility. Suppose they are independent, normal rv's with expected values μ1 = μ2 = 5 and variances σ = 0 =μ100 000 = 25, respectively. a) (4 pts) Let X = = (x1+x2 + ... = ... = +X100)/100. Find the distribution of X. b) (2 pts) Is it necessary to use the central limit theorem to get the resultant distribution in a)? Explain. b) (4 pts) Alan argues that the repair times should be exponentially distributed with the same means and variances given. Find the approximate distribution of X under Alan's assumption.

Let X1, X2, X100 represent the times necessary to perform 100 successive repair tasks at a certain service facility. Suppose they are independent, normal rv's with expected values μ1 = μ2 = 5 and variances σ = 0 =μ100 000 = 25, respectively. a) (4 pts) Let X = = (x1+x2 + ... = ... = +X100)/100. Find the distribution of X. b) (2 pts) Is it necessary to use the central limit theorem to get the resultant distribution in a)? Explain. b) (4 pts) Alan argues that the repair times should be exponentially distributed with the same means and variances given. Find the approximate distribution of X under Alan's assumption.

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.6: Summarizing Categorical Data
Problem 31PPS
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Let X1, X2, X100 represent the times necessary to perform 100 successive repair tasks at a certain service facility. Suppose they are independent, normal rv's with expected values μ1 = μ2 = 5 and variances σ = 0 =μ100 000 = 25, respectively. a) (4 pts) Let X = = (x1+x2 + ... = ... = +X100)/100. Find the distribution of X. b) (2 pts) Is it necessary to use the central limit theorem to get the resultant distribution in a)? Explain. b) (4 pts) Alan argues that the repair times should be exponentially distributed with the same means and variances given. Find the approximate distribution of X under Alan's assumption.
Transcribed Image Text:Let X1, X2, X100 represent the times necessary to perform 100 successive repair tasks at a certain service facility. Suppose they are independent, normal rv's with expected values μ1 = μ2 = 5 and variances σ = 0 =μ100 000 = 25, respectively. a) (4 pts) Let X = = (x1+x2 + ... = ... = +X100)/100. Find the distribution of X. b) (2 pts) Is it necessary to use the central limit theorem to get the resultant distribution in a)? Explain. b) (4 pts) Alan argues that the repair times should be exponentially distributed with the same means and variances given. Find the approximate distribution of X under Alan's assumption.
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