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[Solved] A set of independent measurements are to be taken of a process whose exact distribution is unknown. Through previous experimentation, the distribution

Question: A set of independent measurements are to be taken of a process whose exact distribution is unknown. Through previous experimentation, the distribution of this process is estimated to have a mean of 7 and a variance of 120 . If \(\bar{X}\) denotes the mean of the sample measurements which are to be taken, approximate the number of measurements required such that

\[\operatorname{Pr}(4<\bar{X}<10)=0.866\]

(Hint: Use the central limit theorem).

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