Since \(x = 17\) and \(y = 4\) are each two standard deviations to the right of their means, they represent the same, standardized weight gain relative to their means. CRC Standard Mathematical Tables, 28th ed. normal distribution normal distribution table plot normal distribution sigma1 mu0 References Beyer, W. A negative weight gain would be a weight loss. The so-called 'standard normal distribution' is given by taking and in a general normal distribution. To understand the concept, suppose \(X \sim N(5, 6)\) represents weight gains for one group of people who are trying to gain weight in a six week period and \(Y \sim N(2, 1)\) measures the same weight gain for a second group of people. The z-score allows us to compare data that are scaled differently. Therefore, \(x = 17\) and \(y = 4\) are both two (of their own) standard deviations to the right of their respective means. This means that four is \(z = 2\) standard deviations to the right of the mean.
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