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Measurements on the weight of a lump of metal are believed to be independent and identically dis- tributed; each measurement has mean 12 grams and standard deviation 1.1 gram. a) Find the chance that a single measurement is between 11.8 and 12.2 grams, assuming that individual measurements are normally distributed. b) Estimate the chance that the average of 100 measurements is between 11.8 and 12.2 grams. For this calculation, is it necessary to assume that individual measurements are normally distributed? Explain.

Measurements on the weight of a lump of metal are believed to be independent and identically dis- tributed; each measurement has mean 12 grams and standard deviation 1.1 gram. a) Find the chance that a single measurement is between 11.8 and 12.2 grams, assuming that individual measurements are normally distributed. b) Estimate the chance that the average of 100 measurements is between 11.8 and 12.2 grams. For this calculation, is it necessary to assume that individual measurements are normally distributed? Explain.

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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**Measurements on the weight of a lump of metal are believed to be independent and identically distributed; each measurement has mean 12 grams and standard deviation 1.1 gram.** a) Find the chance that a single measurement is between 11.8 and 12.2 grams, assuming that individual measurements are normally distributed. b) Estimate the chance that the average of 100 measurements is between 11.8 and 12.2 grams. For this calculation, is it necessary to assume that individual measurements are normally distributed? Explain.
Transcribed Image Text:**Measurements on the weight of a lump of metal are believed to be independent and identically distributed; each measurement has mean 12 grams and standard deviation 1.1 gram.** a) Find the chance that a single measurement is between 11.8 and 12.2 grams, assuming that individual measurements are normally distributed. b) Estimate the chance that the average of 100 measurements is between 11.8 and 12.2 grams. For this calculation, is it necessary to assume that individual measurements are normally distributed? Explain.
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