Intro Stats
Intro Stats
4th Edition
ISBN: 9780321825278
Author: Richard D. De Veaux, Paul F. Velleman, David E. Bock
Publisher: PEARSON
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Chapter 2, Problem 46E

Be a Simpson Can you design a Simpson’s paradox? Two companies are vying for a city’s “Best Local Employer” award, to be given to the company most committed to hiring local residents. Although both employers hired 300 new people in the past year, Company A brags that it deserves the award because 70% of its new jobs went to local residents, compared to only 60% for Company B. Company B concedes that those percentages are correct, but points out that most of its new jobs were full-time, while most of Company A’s were part-time. Not only that, says Company B, but a higher percentage of its full-time jobs went to local residents than did Company A’s, and the same was true for part-time jobs. Thus, Company B argues, it’s a better local employer than Company A.

Show how it’s possible for Company B to fill a higher percentage of both full-time and part-time jobs with local residents, even though Company A hired more local residents overall.

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A well-known company predominantly makes flat pack furniture for students. Variability with the automated machinery means the wood components are cut with a standard deviation in length of 0.45 mm. After they are cut the components are measured. If their length is more than 1.2 mm from the required length, the components are rejected. a) Calculate the percentage of components that get rejected. b) In a manufacturing run of 1000 units, how many are expected to be rejected? c) The company wishes to install more accurate equipment in order to reduce the rejection rate by one-half, using the same ±1.2mm rejection criterion. Calculate the maximum acceptable standard deviation of the new process.
5. Let X and Y be independent random variables and let the superscripts denote symmetrization (recall Sect. 3.6). Show that (X + Y) X+ys.
8. Suppose that the moments of the random variable X are constant, that is, suppose that EX" =c for all n ≥ 1, for some constant c. Find the distribution of X.

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