Statistical Techniques in Business and Economics
Statistical Techniques in Business and Economics
18th Edition
ISBN: 9781260788785
Author: Lind, Douglas
Publisher: MCGRAW-HILL HIGHER EDUCATION
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Chapter 15, Problem 61CE

Did you ever purchase a bag of M&M’s candies and wonder about the distribution of colors? Did you know in the beginning they were all brown? Now, peanut M&M’s are 12% are brown, 15% yellow, 12% red, 23% blue, 23% orange, and 15% green. A 6-oz. bag purchased at the Book Store at Coastal Carolina University had 14 brown, 13 yellow, 14 red, 12 blue, 7 orange, and 12 green. Is it reasonable to conclude that the actual distribution agrees with the expected distribution? Use the .05 significance level. Conduct your own trial. Be sure to share with your instructor.

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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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Statistical Techniques in Business and Economics

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