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

Hi Angela, 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.

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Angela Zhang

Last answered:

06 Mar 2023

Posted on:

05 Mar 2023

confused on N(0,1)

in Statistics / Test for the mean. Population variance known

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Eugene YC Lee

Posted on:

06 Mar 2023

confused on N(0,1)

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