Spread of the average output across 25 bakers

Question

A shop employs $25$ bakers whose daily outputs are independent, each with standard deviation $10$ donuts. What is the standard deviation of the average output per baker?

Short answer

$2$ . The variance of a mean of $n$ independent terms with common variance $\sigma^2$ is $\sigma^2/n=100/25=4$ , so the standard deviation is $10/\sqrt{25}=2$ .

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Lessons behind this question

Independence
Covariance and Correlation
Populations, Samples, and Sampling Distributions

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