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?
+36916 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 )
+36916 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 )
