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Scores on the GRE (Graduate Record Examination) are normally distributed with a mean of 581 and a standard deviation of 130. Use the 68-95-99.7 Rule to find the percentage of people taking the test who score below 321.

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%.

Learn more about deviation: https://brainly.in/question/16582667

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