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The distribution of SAT scores is normal with a mean of µ = 500 and a standard deviation of σ = 100. a. What SAT score (i.e., X score) separates the top 15% of the distribution from the rest?b. What SAT score (i.e., X score) separates the top 10% of the distribution from the rest?c. What SAT score (i.e., X score) separates the top 2% of the distribution from the rest?

 Feb 13, 2020

Best Answer 

 #1
avatar+22108 
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Mean = 500        S.D. = 100

 

Look at positive z-score chart   for   .8500   (this would correspond to 85%  )

     my z-score chart shows   z=1.04  corresponds to  .8508

         so 1.04   standard deviations above the mean  is 85 %

                   1.04 x 100 = 104

                           Mean + 104  =  604    would be the score to be in the upper 15%

 

 

For 10 %    find   z-score    .9000    and do similar calc   (closest on my chart is .8997 )

 

For 2%       find z-score    .9800     and do similar calc   (closest on my chart is .9798 )

 Feb 13, 2020
 #1
avatar+22108 
+2
Best Answer

Mean = 500        S.D. = 100

 

Look at positive z-score chart   for   .8500   (this would correspond to 85%  )

     my z-score chart shows   z=1.04  corresponds to  .8508

         so 1.04   standard deviations above the mean  is 85 %

                   1.04 x 100 = 104

                           Mean + 104  =  604    would be the score to be in the upper 15%

 

 

For 10 %    find   z-score    .9000    and do similar calc   (closest on my chart is .8997 )

 

For 2%       find z-score    .9800     and do similar calc   (closest on my chart is .9798 )

ElectricPavlov Feb 13, 2020

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