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QUESTION 4 An astronomer wants to measure the distance from his observatory to a distant star. However, due to atmospheric disturbances, any measurement will not yield the exact distance. As a result, the astronomer has decided to make n series of measurements and then use their average value as an estimate of the actual distance. If the astronomer believes that the values of the successive measurements are independent random variables that follow approximately a normal distribution with a mean of 10 light years and a standard deviation of 2 light years, how many series of measurements he needs to make so that at least 95 percent of the mean distance is less than 9.5 light years?

QUESTION 4 An astronomer wants to measure the distance from his observatory to a distant star. However, due to atmospheric disturbances, any measurement will not yield the exact distance. As a result, the astronomer has decided to make n series of measurements and then use their average value as an estimate of the actual distance. If the astronomer believes that the values of the successive measurements are independent random variables that follow approximately a normal distribution with a mean of 10 light years and a standard deviation of 2 light years, how many series of measurements he needs to make so that at least 95 percent of the mean distance is less than 9.5 light years?

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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QUESTION 4 An astronomer wants to measure the distance from his observatory to a distant star. However, due to atmospheric disturbances, any measurement will not yield the exact distance. As a result, the astronomer has decided to make n series of measurements and then use their average value as an estimate of the actual distance. If the astronomer believes that the values of the successive measurements are independent random variables that follow approximately a normal distribution with a mean of 10 light years and a standard deviation of 2 light years, how many series of measurements he needs to make so that at least 95 percent of the mean distance is less than 9.5 light years?
Transcribed Image Text:QUESTION 4 An astronomer wants to measure the distance from his observatory to a distant star. However, due to atmospheric disturbances, any measurement will not yield the exact distance. As a result, the astronomer has decided to make n series of measurements and then use their average value as an estimate of the actual distance. If the astronomer believes that the values of the successive measurements are independent random variables that follow approximately a normal distribution with a mean of 10 light years and a standard deviation of 2 light years, how many series of measurements he needs to make so that at least 95 percent of the mean distance is less than 9.5 light years?
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