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. A negative weight gain would be a weight loss. 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. To find the z-score for the standard normal distribution that corresponds to the given probability, look up the values in a standard table and find the closest match. The z-score allows us to compare data that are scaled differently. COLLABORATIVE CLASSROOM ACTIVITY Your instructor will record the heights of both men and women in your class, separately. One of special interest is called the standard normal distribution. This means there are an infinite number of normal probability distributions. Therefore, \(x = 17\) and \(y = 4\) are both two (of their own) standard deviations to the right of their respective means. STANDARD NORMAL DISTRIBUTION: Table Values Represent AREA to the LEFT of the Z score. A change in causes the graph to shift to the left or right. This means that four is \(z = 2\) standard deviations to the right of the mean.
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