If is a standard normal deviate, then will have a normal distribution with expected value and standard deviation . This is equivalent to saying that the standard normal distribution can be scaled/stretched by a factor of and shifted by to yield a different normal distribution, called . Conversely, if is a normal deviate with parameters and , then this distribution can be re-scaled and shifted via the formula to convert it to the standard normal distribution. This variate is also called the standardized form of .
If is a standard normal deviate, then will have a normal distribution with expected value and standa.rd deviation . This is equivalent to saying that the standard normal distribution can be scaled/stretched by a factor of and shifted by to yield a d,ifferent normal dis,tribution, called . Conversely, if is a normal deviate with parameters and , then this distribution can be re-scaled and shifted via the formula to convert it to the standard normal distribution. This variate is also called the standardized form of .