EC285 Chapter Notes - Chapter 9: Normal Distribution, Probability Plot, Probability Density Function
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Z-score reports the number of standard deviations away from the mean a value is. In a unimodal, symmetric distribution, about 68% of the values fall within 1 standard deviation of the mean, about 95% fall within 2 standard deviations of the mean, and about 99. 7% fall within 3 standard deviations of the mean. Normal distributions are appropriate models for distributions whose shapes are unimodal and roughly symmetric (cid:1867)(cid:1870)(cid:1865)(cid:1853)(cid:1864) (cid:1871)(cid:1872)(cid:1870)(cid:1854)(cid:1873)(cid:1872)(cid:1867)(cid:1866): (cid:4666),(cid:4667) (cid:1878) (cid:1871)(cid:1855)(cid:1867)(cid:1870)(cid:1857):(cid:1878)=(cid:1877) . Greek letters are used because the mean and the s. d. are not numerical summaries of data. They are numbers that we choose to help specify the distribution, known as parameters. The normal distribution with mean 0 and standard deviation 1 is called the standard normal distribution (standard normal model) When the value doesn"t fall exactly 0, 1, 2, or 3 standard deviations from the mean, we use a table of normal percentiles.
