Answer :
To find the percentage of people taking the GRE who score below 321, we can use the 68-95-99.7 Rule, also known as the empirical rule or the three-sigma rule. Therefore, approximately 10.93% of people taking the GRE score below 321.
This rule states that for a normal distribution:
- Approximately 68% of the data falls within one standard deviation of the mean.
- Approximately 95% of the data falls within two standard deviations of the mean.
- Approximately 99.7% of the data falls within three standard deviations of the mean.
Given:
- Mean (μ) = 581
- Standard deviation (σ) = 130
- Score below (x) = 321
To determine the percentage of people scoring below 321, we need to find the z-score corresponding to this value and then find the area under the curve to the left of that z-score.
The z-score formula is:
z = (x - μ) / σ
Calculating the z-score:
z = (321 - 581) / 130
= -1.2308
Using a standard normal distribution table or a calculator, we can find the area under the curve to the left of z = -1.2308. This area represents the percentage of people scoring below 321.
The area under the curve to the left of z = -1.2308 is approximately 0.1093, or 10.93%.
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