A certain factory produces X, specialized parts on day n, where X, are independent and identically distributed random variables withmean 6 and variance 9. Let Sn be the total number of specialized parts produced from day 1 to day n. Using central limit theorem,determine the total number of parts, a, the said factory can guarantee to produce by day 50 with at least 99.9% certainty, i.e. determinethe maximum value of a so that P(S50 2 a) > 0.999. Note: This maximum value must be a whole number.

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A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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2. A certain factory produces X, specialized parts on day n, where X, are independent and identically distributed random variables with mean 6 and variance 9. Let S„be the total number of specialized parts produced from day one to day n. Using Central Limit Theorem, determine the total number of parts, a, the said factory can guarantee to produce by day 50 with at least 99.9% certainty, i.e., determine the maximum value of a so that P(S50 2 a) > 0.9999. Note that this maximum value must be a whole number
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