6. One hundred numbers are rounded to the nearest integer and then added to- gether. Assuming round-off errors are independent and identically distributed as Unif(-1/2, 1/2) random variables, use the Central Limit Theorem to show that there is about a 27% chance that the sum of the rounded numbers and the sum of unrounded numbers will differ by at most 1.

6. One hundred numbers are rounded to the nearest integer and then added to- gether. Assuming round-off errors are independent and identically distributed as Unif(-1/2, 1/2) random variables, use the Central Limit Theorem to show that there is about a 27% chance that the sum of the rounded numbers and the sum of unrounded numbers will differ by at most 1.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter10: Sequences, Series, And Probability

Section10.8: Probability

Problem 31E

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