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Mean and standard deviation

 
 
tmt2114
 
Reply Wed 6 Jun, 2012 01:20 pm
One test has a mean of 100 and a standard deviation of 15. What percentage of students would have a test score of 115 or more when given the test?
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JPB
 
  2  
Reply Wed 6 Jun, 2012 01:42 pm
@tmt2114,
You'll need to know if the data are normally distributed. If yes, then you want the area under the curve of the normal distribution with a Z-score greater than 1.0.
laughoutlood
 
  1  
Reply Wed 6 Jun, 2012 07:56 pm
@JPB,
(x - mu ) / sigma , is mostly greek to me
raprap
 
  1  
Reply Wed 6 Jun, 2012 08:50 pm
@laughoutlood,
mu and sigma are greek

OK mu is the average (100); sigma ia the stabdard deviation(15); and x is value you want (115)

Put these values in to determine z z=(x-mu)/sigma

Now go to the standard deviation table--the total area under this curve is the entire population (1), the fraction you are looking for is the area under the curve for all z greater than the z you calculate. On a standard normal population table you'll have a chart for the area under the curve less than that z. That is the fraction of the population less than that z (it will be less than 1).

But you are interedted in the fraction of the population greater than that z.

No problemo---the total value of the population is 1 (a certainity). The fraction less is given on the table for that z---so the fraction greater is 1 minus the table value (it will also be less than 1).

Check--if you get any answer that is not between zero and one you're doing something wrong.

Rap
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Lustig Andrei
 
  1  
Reply Wed 6 Jun, 2012 09:02 pm
When y'all decide to commence communicating in English, let me know. I'll come back.
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