A certain factory produces Xn specialized parts on day n, where Xn 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 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. determine the maximum value of a so that P(S50 ≥ a) ≥ 0.999. Note: This maximum value must be a whole number.

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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A certain factory produces Xn specialized parts on day n, where Xn 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 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. determine the maximum value of a so that P(S50 ≥ a) ≥ 0.999. Note: This maximum value
must be a whole number.
Transcribed Image Text:A certain factory produces Xn specialized parts on day n, where Xn 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 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. determine the maximum value of a so that P(S50 ≥ a) ≥ 0.999. Note: This maximum value must be a whole number.
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