When we calculate a z-score for a statistic, as in Question 1, Part B, we call this a standardized statistic. Question 1 used simulation to estimate the mean and standard deviation of the sample mean. Mathematically, though, we know the exact formulas for these values. The standardized sample mean is z = x [ m e a n o f x ] s t d . d e v i a t i o n o f x = x n where x is the sample mean, is the population mean, is the population standard deviation, and n is the sample size. The statistic is "standardized" since it is centered to have a mean of 0 and scaled to have a standard deviation of 1. If the population distribution is normal or the sample size is sufficiently large, this standardized statistic will follow a standard normal distributiona normal distribution with a mean of 0 and a standard deviation of 1