SOLUTION: Scores on the GRE (Graduate Record Examination) are normally distributed with a mean of 530 and a standard deviation of 88. Use the 68-95-99.7 Rule to find the percentage of people

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Question 1039491: Scores on the GRE (Graduate Record Examination) are normally distributed with a mean of 530 and a standard deviation of 88. Use the 68-95-99.7 Rule to find the percentage of people taking the test who score between 266 and 794.
The answer is 99.7% but I don't understand or know how to get that.
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
The mean is 530
1 standard deviation below the mean is 530-88 = 442
2 standard deviations below the mean is 442-88 = 354
3 standard deviations below the mean is 354-88 = 266

So 266 is 3 standard deviations below the mean.

The mean is 530
1 standard deviation above the mean is 530+88 = 618
2 standard deviations above the mean is 618+88 = 706
3 standard deviations above the mean is 706+88 = 794

So 794 is 3 standard deviations above the mean.

On this graph:



0 on the horizontal z-axis represents the mean, 530
-1 on it represents 1 standard deviation below the mean, 442.
-2 on it represents 2 standard deviations below the mean or 354.
-3 on it represents 3 standard deviations below the mean or 266.
1 on it represents 1 standard deviation above the mean, 618.
2 on it represents 2 standard deviations above the mean or 706.
3 on it represents 3 standard deviations above the mean or 794.

The EMPIRICAL RULE (or the 68-95-99.7 Rule) says that about 68% of the data is between
1 standard deviation below the mean and 1 standard deviation above
the mean.  Below the shaded part is about 68% of the area between
the normal curve and the z-axis.



The EMPIRICAL RULE (or the 68-95-99.7 Rule) also says that about 95%
of the data is between 2 standard deviations below the mean and 2 
standard deviations above the mean.  Below the shaded part is about 
95% of the area between the normal curve and the z-axis.



The EMPIRICAL RULE also says that about 99.7% of the data is between
3 standard deviations below the mean and 3 standard deviations above
the mean.  Below the shaded part is about 99.7% of the area between
the normal curve and the z-axis.  (That's roughly ALL of it!)



Edwin