Scores on the GRE are normally distributed with a mean of 541 and a standard deviation of 89. Use the 68-95-99.7 rule to find the percentage of people who score between 363 and 541
well, 363 is 2 std below the mean. So, apply your rule.
To find the percentage of people who score between 363 and 541 on the GRE, we can use the 68-95-99.7 rule.
According to this rule, approximately 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.
First, let's calculate the z-scores for both 363 and 541.
z-score = (x - mean) / standard deviation
For 363:
z-score = (363 - 541) / 89 = -1.998
For 541:
z-score = (541 - 541) / 89 = 0
Now we need to find the percentage of data between these two z-scores.
Using a standard normal distribution table (also known as a z-table) or a calculator with built-in statistical functions, we can find the areas under the curve corresponding to the z-scores, and subtract the smaller value from the larger value.
The area between -1.998 and 0 represents the percentage of people who score between 363 and 541.
By looking up the z-scores in a z-table, we find that the area to the left of -1.998 is approximately 0.0228, and the area to the left of 0 is 0.5.
To find the area between these two z-scores, we subtract the smaller area from the larger area:
0.5 - 0.0228 = 0.4772
Therefore, approximately 47.72% of people score between 363 and 541 on the GRE.