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3-4 example2 - Student Grady Silnonton Course Math119...

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Unformatted text preview: Student: Grady Silnonton Course: Math119: Elementary Statistics - Spring 2010 - CRN: 49239 Instructor: Shawn Par'vini - 16 weeks Date: 2/18/10 Book: Triola: Elementary Statistics, 11e Time: 1:55 PM A particular group of men have heights with a mean of 180 cm and a standard deviation of 5 cm. Earl had a height of 182 cm. a. What is the difference between Earl‘s height and the mean? I}. How many standard deviations is that [the difference found in part (a)]? c. Convert Earl's height to a z score. d. If we consider "usual" heights to be those that convert to z scores between — 2 and 2, is Earl‘s height usual or unusual? a. To find the difference between Earl's height and the mean, subtract the smaller value from the larger value. 182 cm — 180 cm =2 cm b. To determine how many standard deviations the difference is, compare the difference, 2, to the standard deviation, 5. 2 g = 0.4 standard deviations c. A z score is the number of standard deviations that a given value x is above or below the mean. It is found using the following expressions. Sample Population x-x x-u or z: s o z: x—u o The group of men is a population. Therefore, to convert Earl's height to a z score, use the formula 2 = . Substitute the appropriate values into the formula. x-u_182-180 z: o 5 Simplify to get the z score. 182 - 180 z = T = 0.4 d. The 2 score is 0.4. Since "usual" heights are considered to be those that convert to z scores between — 2 and 2, Earl's height is usual. Page 1 ...
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