An engineer is measuring a quantity 0. It is assumed that there is a random error in each measurement, so the engineer will take n measurements and report the average of the measurements as the estimated value of 0. Here, n is assumed to be large enough so that the central limit theorem applies. If X, is the value that is obtained in the ith measurement, we assume that X; = 0 + W, where W, is the error in the ith measurement. We assume that the W,'s are i.i.d. with EW, = 0 and Var(") = 4 units. The engineer reports the average of the measurements X, + X2+...+X, X = How many measurements does the engineer need to make until he is 90% sure that the final error is less than 0.25 units? In other words, what should the value of n be such that P(0 – 0.25 < X <0 + 0.25) 2 .90?
An engineer is measuring a quantity 0. It is assumed that there is a random error in each measurement, so the engineer will take n measurements and report the average of the measurements as the estimated value of 0. Here, n is assumed to be large enough so that the central limit theorem applies. If X, is the value that is obtained in the ith measurement, we assume that X; = 0 + W, where W, is the error in the ith measurement. We assume that the W,'s are i.i.d. with EW, = 0 and Var(") = 4 units. The engineer reports the average of the measurements X, + X2+...+X, X = How many measurements does the engineer need to make until he is 90% sure that the final error is less than 0.25 units? In other words, what should the value of n be such that P(0 – 0.25 < X <0 + 0.25) 2 .90?
Mathematics For Machine Technology
8th Edition
ISBN:9781337798310
Author:Peterson, John.
Publisher:Peterson, John.
Chapter29: Tolerance, Clearance, And Interference
Section: Chapter Questions
Problem 11A
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