SOLUTION: Again I am unsure where to place this question but any help would be amazing. Assume that a normal distribution of data has a mean of 11 and a standard deviation of 2. Use the 6

Question 891156: Again I am unsure where to place this question but any help would be amazing.
Assume that a normal distribution of data has a mean of 11 and a standard deviation of 2. Use the 68-95-99.7 Rule to find the percentage of values that lie above 9.
What percentage of values lie above 9?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
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.

$$$

the 68-95-99 rule is an approximation.

the calculations shown in the picture are more exact.

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