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Suppose X follows a normal distribution with mean=1 and variance=4. Let's randomly select 4
numbers from X. What is the distribution of the mean of these four numbers? What is the
probability that the mean is between -1 and 1?
Solution
The distribution of mean is also normal distribution with mean 1 and variance 1
Probability that the mean is between -1 and 1 is 0.47725

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Suppose X follows a normal distribution with mean=1 and variance=4. .pdf

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