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?

MATLAB: An Introduction with Applications
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ISBN:9781119256830
Author:Amos Gilat
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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: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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