confused on N(0,1)
Could you explain why the original formula of Z obtain a distribution with a mean of 0, and a sd of 1? Please elaborate on where these numbers come from? Thanks
If X is a normally distributed random variable with mean mu and standard deviation sigma, then by the transformation (or standardization) Z = (X - mu)/sigma , the distribution of Z is normally distributed with mean 0 and standard deviation 1 (the definition of standard normal random variate).
In the lecture, we are dealing with the random variable X_bar, whose mean is mu and standard deviation sigma / sqrt(n), hence, Z = (X_bar - mu)/(sigma/sqrt(n)) is a standard normal random variate.
Hope this helps.