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According to the central limit theorem, when you take many samples, the distribution of the sample means center/average around the population mean, with standard deviation = pop standard dev / square root of sample size.

The problem below is from an R course, which asks

"What does the CLT tell us is the mean of (you don't need code)?

1) I would think that the mean of Z is the population mean ux? But it is 0?

2) What is the notation here? for Z= ? Is that the notation for a distribution? Until now distributions have just been descibed as having mean and stdev ,there was no z =

  1. What would the standard deviation of the population be? Can i assume the stdev of this distrubtion is 1? But why when there is no summing of variance from the two populations like in a t distrbution?
Kevin Lee
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  • it should be like `N(kμ,k^2σ)` where `k = sqrt(12)` In this case initially `Z was N(0,1)` therefore mean would be 0 and standard deviation would be 12. – RakeshV Jul 26 '20 at 13:16
  • Good question, but this is off topic for SO, try stats.stackexchange.com instead. – Robert Dodier Jul 28 '20 at 16:41

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