Scores on the GRE (Graduate Record Examination) are normally distributed with a mean of 554 and a standard deviation of 120. Use the 68-95-99.7 Rule to find the percentage of people taking the test who score between 434 and 674
It is ± 1 SD. Use the rule.
PsyDAG, is it 68/2=34 or
100-68=32 or
68%
Please explain, I'm confused on this part. Thanks
68%
To use the 68-95-99.7 Rule, also known as the empirical rule, we need to understand that it applies to a normal distribution. In a normal distribution, approximately:
- 68% of the data falls within one standard deviation of the mean,
- 95% within two standard deviations, and
- 99.7% within three standard deviations.
In this case, we know that the mean GRE score is 554, and the standard deviation is 120.
First, let's calculate the z-scores for the given scores using the formula:
z = (x - μ) / σ
where:
x = the score
μ = the mean
σ = the standard deviation
For the lower score, 434:
z1 = (434 - 554) / 120
z1 = -1
For the upper score, 674:
z2 = (674 - 554) / 120
z2 = 1
Now, we can use the z-scores to find the percentage of people who score between these two values.
- To find the percentage of people who score below 434, we find the area to the left of z = -1. This area is 0.1587 or 15.87%.
- To find the percentage of people who score below 674, we find the area to the left of z = 1. This area is 0.8413 or 84.13%.
Finally, to find the percentage of people who score between 434 and 674, we subtract the percentage below 434 from the percentage below 674:
Percentage = 84.13% - 15.87% = 68.26%
Therefore, approximately 68.26% of people taking the GRE test score between 434 and 674.