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lets talk about standardizing normally distributed random variables suppose X is a normally distributed random variable with mean mu and standard deviation sigma which we sometimes right notation wise as X is distributed normally with a mean of mu and a variance of sigma squared this is not universal notation but it is pretty standard X is distributed normally with a mean of mu and the second term is the variance sigma squared with a standard deviation of sigma of course now suppose we want to standardize this. In other words turned it into something that has any standard normal distribution which is a normal distribution with a mean of zero and a standard deviation of one how would we do that? well lets think X has a mean of mu, so if we go x minus mu then this quantity is going to have a mean of zero and if we divide by sigma then this whole all quantity is going to have a standard deviation of one. This is a basic linear transformation and we force this quantity to have a mean
