4 ms·
CLT is about the sum. In your case, the sum of heights will still converge to the normal distribution of you take the height of n random people (man or woman)
by elcomet 7y ago
CLT is about the sum.
In your case, the sum of heights will still converge to the normal distribution of you take the height of n random people (man or woman)
- BeetleB 7y ago> In your case, the sum of heights will still converge to the normal distribution of you take the height of n random people (man or woman) Yes and no. The sample must be independent and identically distributed. In your case the "identical" part is not correct, as men and women have different distributions (both are normal but with different mean and std). However, if both distributions are normal, then their sum is normal (even with different mean and std). The fact that the sum is normal in this case has nothing to do with the CLT - it's just a quirk of the normal distribution that the sum is normal. Had men/women had non-normal distributions with different means/stds, then the sum would not be normal.