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?

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Question

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) > .90?

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can you explain ? thank you !

By our discussion above, the 95% Confidence
interval for 0 = Ex; is given by
6
(x - 2 € √ X + 25 ²5 ).
-
ท

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