(x) Points: 0 of 1
Save
Scores on the GRE (Graduate Record Examination) are normally distributed with a mean of 593 and a standard deviation of 133. Use the 68-95-99.7 Rule to find the percentage of people taking the test who score between 194 and 593.

The percentage of people taking the test who score between 194 and 593 is $\square \%$.

Step 1 ：The 68-95-99.7 rule, also known as the empirical rule, states that for a normal distribution, 68% of the data falls within one standard deviation of the mean, 95% falls within two standard deviations, and 99.7% falls within three standard deviations.

Step 2 ：In this case, we are asked to find the percentage of people who score between 194 and 593. We know that the mean is 593 and the standard deviation is 133.

Step 3 ：Therefore, we need to calculate how many standard deviations away 194 is from the mean. This will allow us to use the empirical rule to find the percentage of people who score within this range.

Step 4 ：The score of 194 is 3 standard deviations away from the mean. According to the empirical rule, 99.7% of the data falls within three standard deviations of the mean.

Step 5 ：However, this includes data on both sides of the mean. Since we are only interested in scores between 194 and 593 (i.e., scores less than or equal to the mean), we need to consider only half of this percentage.

Step 6 ：Final Answer: The percentage of people taking the test who score between 194 and 593 is \( \boxed{49.85\%} \).