Question 891156
68 is within 1 standard deviation.
95 is within 2 standard deviations.
99 is within 3 standard deviations.


i believe that's the rule.


you have a mean of 11 and a standard deviation of 2.


you want to find the percentage of values that lie above 9.


your z score is equal to (x-m/s where x = 9, m = 11, s = 2


you get:


z = (9 - 11) / 2 = -2/2 = -1.


your z score is 1 standard deviation below the mean.


this would fall under the 68 rule, except you can't use the rule as is.


you have to do some logical analysis.


68% of the data is within 1 standard deviation from the mean.


this means the z score of the data has a low value of -1 and a high value of +1


so 68% of the data is between a z score of -1 and a z score of 1.


this means that 32% of the data lies outside this range.


this is evenly split between the low side and the high side.


this means that 16% of the data lies below a standard deviation of -1 and 16% of the data lies above a standard deviation of 1.


your data has a z score of -1


this means that 16% of your data lies below a z score of -1 and 68% + 16% = 84% of your data lies above a z score of -1.


they want to know the percentage of values that lie above 9.


that would be 84%


here's a picture of what I mean.


<img src = "http://theo.x10hosting.com/2014/080501.jpg" alt="$$$" </>


the 68-95-99 rule is an approximation.


the calculations shown in the picture are more exact.