A random variable ? is the output of an engineering process, and ? is uniformly distributed. The PDF of ? is equal to 1/10 for any positive x smaller than or equal to 10, and it is 0 otherwise. If you take a random sample of 30 observations, what is the approximate probability distribution of ?̅ − 3? (You need to find the mean and variance of this quantity and state your assumptions)

A First Course in Probability (10th Edition)
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Author:Sheldon Ross
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Chapter1: Combinatorial Analysis
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A random variable ? is the output of an engineering process, and ? is uniformly
distributed. The PDF of ? is equal to 1/10 for any positive x smaller than or equal to 10, and it is 0
otherwise. If you take a random sample of 30 observations, what is the approximate probability
distribution of ?̅ − 3? (You need to find the mean and variance of this quantity and state your
assumptions)

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