Question

Scores on the GRE (Graduate Record Examination) are normally distributed with a mean of 594 and a standard deviation of 96. Use the 68-95-99.7 Rule to find the

percentage of people taking the test who score below 306.

The percentage of people taking the test who score below 306 is

%.

Answer 1

0.15%

Explanation:

The Empirical Rule ( 68-95-99.7 Rule) states that almost all data falls within 3 standard deviations of the mean for a normal distribution. Under the rule:

1. 68% of the data falls within one standard deviation.
2. 95% percent of the data lies within two standard deviations.
3. 99.7% of data fall within three standard deviations

Given that:

mean (μ) = 594 and standard deviation σ = 96

1. 68% of the data falls within μ ± σ. That is 594 ± 96. 68% fall within 498 and 690
2. 95% percent of the data lies within μ ± 2σ. That is 594 ± 2(96). 95% fall within 402 and 786
3. 99.7% percent of the data lies within μ ± 3σ. That is 594 ± 3(96). 99.7% fall within 306 and 882

The percentage of people that all fall outside 306 and 882 = 100% - 99.7% = 0.3%. Therefore the percentage of people that are below 306 = 0.3% / 2 = 0.15%