Essentials of Modern Business Statistics with Microsoft Office Excel (Book Only)
Essentials of Modern Business Statistics with Microsoft Office Excel (Book Only)
7th Edition
ISBN: 9781337681643
Author: David R. Anderson; Dennis J. Sweeney; Thomas A. Williams
Publisher: Cengage Learning US
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Chapter 6.2, Problem 15E

(a)

To determine

To find: The value of z .

(b)

To determine

To find: The value of z .

(c)

To determine

To find: The value of z .

(d)

To determine

To find: The value of z .

(e)

To determine

To find: The value of z .

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iid 1. The CLT provides an approximate sampling distribution for the arithmetic average Ỹ of a random sample Y₁, . . ., Yn f(y). The parameters of the approximate sampling distribution depend on the mean and variance of the underlying random variables (i.e., the population mean and variance). The approximation can be written to emphasize this, using the expec- tation and variance of one of the random variables in the sample instead of the parameters μ, 02: YNEY, · (1 (EY,, varyi n For the following population distributions f, write the approximate distribution of the sample mean. (a) Exponential with rate ẞ: f(y) = ß exp{−ßy} 1 (b) Chi-square with degrees of freedom: f(y) = ( 4 ) 2 y = exp { — ½/ } г( (c) Poisson with rate λ: P(Y = y) = exp(-\} > y! y²
2. Let Y₁,……., Y be a random sample with common mean μ and common variance σ². Use the CLT to write an expression approximating the CDF P(Ỹ ≤ x) in terms of µ, σ² and n, and the standard normal CDF Fz(·).
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