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Suppose when a signal having unknown value μ is transmitted from node A, the value received at node B is normally distributed with mean μ and variance 5. In other words, when the signal is sent, then its value received is μ + W where W represents a Gaussian noise with mean 0 and UNKNOWN VARIANCE. To reduce an error, suppose 16 redundant signals of the same value μ are sent. Upon their receipt at node B, their values were recorded as 2 4 7 3 12 11 5 6 16 14 1 3 9 2 4 1 (a) Construct a 95% confidence interval for μ. (b) How large must n be so that the confidence interval has a margin of error of 0.2? (c) There is a filter that can reduce the variance of the noise to 1. If the daily cost of the filter is $1 and the daily cost of each additional redundant signal (above 16) is $0.01, which of the following options is more economical? • Buy the filter and add redundant signals if needed to achieve a margin of error of 0.2 • Do not buy the filter, but add redundant signals to achieve a margin of error of 0.2

Rabia S.