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. ![]() It does this for positive values of z only (i.e., z-values on the right-hand side of the mean). A negative weight gain would be a weight loss. The standard normal distribution table provides the probability that a normally distributed random variable Z, with mean equal to 0 and variance equal to 1, is less than or equal to z. Z Score Table- chart value corresponds to area below z score. 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 first column of the table shows the whole. The z-score allows us to compare data that are scaled differently. Examine the table and note that a 'Z' score of 0.0 lists a probability of 0.50 or 50, and a 'Z' score of 1, meaning one standard deviation above the mean, lists a probability of 0.8413 or 84. A standard normal distribution table shows a cumulative probability associated with a particular z-score. ![]() 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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