Popular in Statistics for Biosciences
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This 3 page Class Notes was uploaded by Darko Stoilkovski on Tuesday October 13, 2015. The Class Notes belongs to STP 231 at Arizona State University taught by in Fall 2015. Since its upload, it has received 59 views. For similar materials see Statistics for Biosciences in Statistics at Arizona State University.
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Date Created: 10/13/15
ZScore o Zscore tells us how many standard deviations above or below the mean is a particular value 0 ZXHO 0 Unit of measurement does not affect the zscore value 0 Zscores have a mean of 0 and a standard deviation of 1 0 Most zscores are between 3 and 3 o This tells us how many standard deviations the value is away from the mean Negative is below mean Positive is above mean Example Zscore 0 Most college career counselors agree that starting salary is associated with academic major Even if a person s first job is not directly related to their course of study their salary might still be related to their academic major A recent survey of academic major and starting salary of graduates showed the following information mnem Standard Deviation English 32300 1175 Computer 42500 2375 Science 0 A Computer Science major who responded to the survey received a starting salary of 45000 and an English major received an offer of 35000 Which salary is better in terms of statistics Solution 0 For computer science major the zscore is 0 Z x p o 45000 425000 2375 105 This means 45000 is 105 standard deviations above the mean 0 For English major the zscore is 0 Z 3500032300 1175 230 This means 35000 is 230 standard deviations above the mean I We conclude the English major s starting salary is actually better because the salary is much higher than those of most English majors Normal Distribution 0 Normal distribution Avariable is normally distributed if its distribution has the shape of a symmetric curve 0 Normal distribution is characterized by its mean u and standard deviation 0 o The mean u and standard deviation 0 are known as parameters of the normal distribution 0 Change in mew shifts graph left or right 0 Change in sigma makes graph narrower or wider Narrower taller graph Wider shorter graph Normal Curve 63 M data 39iquot 5501 data QMquot Dll data Finding Probabilities Using a Normal Curve 0 Transform a given normal distribution with mean u and standard deviation 0 into a standard normal distribution 0 To complete the transformation for each value x we perform the following operations 0 ZXH0 Standard Normal Curve Bell curve a mean of l Standard deviation of 139
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