8-5 - 8-5 Normal Distributionscontinuous distribution found...

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Unformatted text preview: 8-5 Normal Distributionscontinuous distribution found in many application areas e.g. SAT scores, peoples heights, leaf lengths all are distributed according to the normal distributionalso called the Gaussian Distributionit is the famous "bell-shaped" curve:distributions have a mean and a standard deviation the above Normalhas = 430 and = 100 For any Normal Distributionwith mean and standard deviation : 68% of all scores lie within 1of the mean 95% are within 299.7% (virtually all) are within 38-5p. 1Computing areas (probabilities) under normal distributionsQuestion:What % of the people that take the SAT make scores between 330 and 530? Analysis:mean = 430 s.d. = 100 picture: 330 = -530 = + % of scores between -and + for any normal distribution? We know that one; it's 68% !!!8-5p. 2Question:What % of the people that take the SAT make scores between 430 and 600? Analysis:mean = 430 s.d. = 100 600 = how many from the mean?z = 100430600-= 1.7We only knowpercentages for within 1,2and 3of the mean. Q: Can we find the area under a normal from to + 1.7A: Yes, we can look it up in a table. Here's the picture: z = 1.7The table on page 723: gives us area (for any normal distribution!!!) from to + (any number of ) look up 1.7 .4554Answer: 45.56% 8-5p. 3Z-statisticsby computing the number of 's a score is from the mean you are computing a number known as: a z-statistic, or a standardized scorethe unit of measurement of a z-statisticis always standard deviationsExample:if = 10 and = 7, what is the z-statisticor standardized scorecorresponding to a score of 15?...
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This note was uploaded on 12/11/2011 for the course MATH 1324 taught by Professor Staff during the Spring '11 term at Austin Community College.

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8-5 - 8-5 Normal Distributionscontinuous distribution found...

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