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Unformatted text preview: The standard Normal distribution As the 68–95–99.7 rule suggests, all Normal distributions share many properties. In fact, all Normal distributions are the same if we measure in units of size σ about the mean μ as center. Changing to these units is called standardizing. To standardize a value, subtract the mean of the distribution and then divide by the standard deviation . If x is an observation from a distribution that has mean μ and standard deviation σ , the standardized value of x is A standardized value is often called a z-score. A z-score tells us how many standard deviations the original observation falls away from the mean , and in which direction. Observations larger than the mean are positive when standardized, and observations smaller than the mean are negative Standardizing women’s heights The heights of women aged 20 to 29 are approximately Normal with...
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- Fall '11
- Normal Distribution, standard deviations, normal distributions