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A supplier of paper produces 10-sheet packs of certain high gloss paper for the production of brochures. For a publishing project we need 205 sheets and so purchase 21 packs. Due to manufacturing imperfections the packs do not always contain 10 sheets. If we denote by X; the number of sheets of paper in the ith pack then (0.1 if k = 9 0.8 if k = 10 P(X₁ = k) = 0.1 if k = 11 0 if k {9, 10, 11}. We further assume that the random variables X; are independent. (a) Find the mean and standard deviation of Xi. (b) Denote by X the total number of paper sheets we have purchased, X = X₁++X21. Calculate the mean and standard deviation of X. (c) Estimate the probability that we have purchased enough sheets for our project, 205). You should use the continuity correction. i.e. P(X

A supplier of paper produces 10-sheet packs of certain high gloss paper for the production of brochures. For a publishing project we need 205 sheets and so purchase 21 packs. Due to manufacturing imperfections the packs do not always contain 10 sheets. If we denote by X; the number of sheets of paper in the ith pack then (0.1 if k = 9 0.8 if k = 10 P(X₁ = k) = 0.1 if k = 11 0 if k {9, 10, 11}. We further assume that the random variables X; are independent. (a) Find the mean and standard deviation of Xi. (b) Denote by X the total number of paper sheets we have purchased, X = X₁++X21. Calculate the mean and standard deviation of X. (c) Estimate the probability that we have purchased enough sheets for our project, 205). You should use the continuity correction. i.e. P(X

A First Course in Probability (10th Edition)
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 supplier of paper produces 10-sheet packs of certain high gloss paper for the production of brochures. For a publishing project we need 205 sheets and so purchase 21 packs. Due to manufacturing imperfections the packs do not always contain 10 sheets. If we denote by X; the number of sheets of paper in the ith pack then (0.1 if k = 9 0.8 if k = 10 P(X₁ = k) = 0.1 if k = 11 0 if k {9, 10, 11}. We further assume that the random variables X; are independent. (a) Find the mean and standard deviation of Xi. (b) Denote by X the total number of paper sheets we have purchased, X = X₁++X21. Calculate the mean and standard deviation of X. (c) Estimate the probability that we have purchased enough sheets for our project, 205). You should use the continuity correction. i.e. P(X
Transcribed Image Text:A supplier of paper produces 10-sheet packs of certain high gloss paper for the production of brochures. For a publishing project we need 205 sheets and so purchase 21 packs. Due to manufacturing imperfections the packs do not always contain 10 sheets. If we denote by X; the number of sheets of paper in the ith pack then (0.1 if k = 9 0.8 if k = 10 P(X₁ = k) = 0.1 if k = 11 0 if k {9, 10, 11}. We further assume that the random variables X; are independent. (a) Find the mean and standard deviation of Xi. (b) Denote by X the total number of paper sheets we have purchased, X = X₁++X21. Calculate the mean and standard deviation of X. (c) Estimate the probability that we have purchased enough sheets for our project, 205). You should use the continuity correction. i.e. P(X
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