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posted by  frankieandmax on 10/13/2008 12:51:18 PM  |  status: Live  

Standard deviation help ASAP

Course Textbook Chapter Problem
Statistics and Probability N/A N/A N/A
Question Details:
Paul received a score of 80 on a history test for which the class mean was 70 and standard deviation was 10.  He received a score of 75 on a biology test where the class mean was 70 and standard devation was 2.5.  Which test did he do better relative to the rest of the class???
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posted by IKM on 10/13/2008 1:06:55 PM  |  status: Live
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Response Details:
hello,
using area property of normal distribution:
the history class having (μ±σ) = (70±10) = (60 80) (covers atmost 68% OF CLASS)
where the 80 marks are obtained by paul
where as forbiology class we have (μ±2σ) = (70±2(2.5)) = (65 75) (covers atmost 95% of class)
where 75 marks are obtained by paul
hence from the above statements it is clear that biology test have better result than history test result
 
hope this will help you
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posted by Anonymous on 10/13/2008 1:07:56 PM  |  status: Live
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Response Details:
The problem is using the zscore or the number of standard deviations away from the mean as a measure of the performance.
First the history test, the z score or z=(x-mu)/sigma=(80-70)/10 = 1. This means that pauls score was exactly 1 standard deviation above the mean or approximately 84th percentile.
 
For the biol test the same procedure gives z=(75-70)/2.5 or 2. This is much better performance and the approxmiate percetile is 98.
 
The key point of this exercise is to know that if you have a normal distribution, then the z value (as computed above) give the position on the normal distribution which in turn gives the percentage of the population that is below this particular value
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