4. An astronomer wants to approximate the distance d (in light years) from Earth to a distant star using a certain measuring device. To obtain an esimate, she makes a series of measurements and then takes the average d. She believes that measurement errors are not systematic, and hence each measurement can reasonably be modeled as an independent random variable with mean d, the true (unknown) distance, and a variance of 4 light years squared (that is, the standard deviation is o = 2 light years). Using the Central Limit Theorem, determine the number of measurements n required in order to be approximately 95% sure that the estimated distance d is accurate to within +0.5 light years of the true distance d.

4. An astronomer wants to approximate the distance d (in light years) from Earth to a distant star using a certain measuring device. To obtain an esimate, she makes a series of measurements and then takes the average d. She believes that measurement errors are not systematic, and hence each measurement can reasonably be modeled as an independent random variable with mean d, the true (unknown) distance, and a variance of 4 light years squared (that is, the standard deviation is o = 2 light years). Using the Central Limit Theorem, determine the number of measurements n required in order to be approximately 95% sure that the estimated distance d is accurate to within +0.5 light years of the true distance d.

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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