## Z-score

When a data set is assumed to be governed by a normal density function with parameters and , we say ``it is normally distributed with mean and standard deviation ,'' for which we often simply write . In particular we call the standard normal distribution. Suppose that a value in data is normally distributed with (here is also referred to a ``normal random variable''). ThenExample. Suppose that you scored 650 on SAT in 2000, and 30 on ACT in 2001. The SAT exam in 2000 had mean 500 and standard deviation 100, and the ACT had mean 21 and standard deviation 4.3. How can you compare these scores? Can you say you did it better in 2001?