An engineer is measuring a quantity q. It is assumed that there is a random error in each measurement, so the engineer will take n measurements and reports the average of the measurements as the estimated value of q. Specifically, if Y_i is the value that is obtained in the i'th measurement, we assume that Y_i = q +X_i, where X_i is the error in the ith measurement. We assume that X_i's are i.i.d. with EX_i = 0 and Var(X_i) = 4 units. The engineer reports the average of measurements

How many measurements does the engineer need to make until he is 95% sure that the final error is less than 0.1 units? In other words, what should the value of n be such that

Transcribed Image Text:

Mn Y₁+Y₂+...+Yn n