find the percentage of people taking the test who score below 311

Question

Scores on the GRE (Graduate Record Examination) are normally distributed with a mean of 579 and a standard deviation of 134. Use the 68 - 95 - 99.7. Rule to find the percentage of people taking the test who score below 311

Answer 1

Hi Sapphron.

 

If I could draw the normal curve, this would be easier...

 

Start with the mean, 579, then add 1 standard deviation to it (add 134 to the mean), and subtract 1 standard deviation (subtract 134 from the mean).  This range of values:  445 to 713  is the 68 in the 68-95-99.7 rule, meaning 68% of all the GRE scores will be between 445 and 713.  The number you are looking for, 311, is NOT in this range, so we need to go out more from the mean.

 

If we go out one more standard deviation, (mean - 2 sd) and (mean + 2 sd), we find that this larger range  is 311 - 847, this is the 95 in the 68-95-99.7 rule.  In other words, 95% of the GRE scores will be between 311 and 847.

 

So we have found the number we are looking for, the 311.   If we want to know the percentage of scores BELOW that, They will be in the remaining 5% of the GRE Scores.   But they are not the full 5%, because the bell-shaped curve is symmetric around the mean, only half of the remaining scores will be below 311, and the other half of the remaining scores will be above 847.  So half of 5% is 2.5%, and that is your answer.

 

Final Answer:  2.5%