Question

Scores on the GRE (Graduate Record Examination) are normally distributed with a mean of 513 and a standard deviation of 82. Use the 68-95-99.7 Rule to find the percentage of people taking the test who score between 513 and 759. The percentage of people taking the test who score between 513 and 759 is %

Answer 1

Answer:

Note that we need calculate the scores between the mean ($\mu=513$) and the mean plus 3 times the standard deviation. It is 3 times since the distance between the values given (513 and 759) divided by the standard deviation is 3 ($\frac{759-513}{82}=3$)

So the rule say that 99.7% of data is between $\mu - 3\sigma$ and $\mu + 3\sigma$, as it is a normal distribution half of 99.7% is between $\mu$ and $\mu+3\sigma$. Hence 49.85% of people score between 513 and 759.