## Scores on the GRE are normally distributed with a mean of 514 and a standard deviation of 92. Use the 68-95-99.7 rule to find the percentage

Question

Scores on the GRE are normally distributed with a mean of 514 and a standard deviation of 92. Use the 68-95-99.7 rule to find the percentage of people taking the test who score above 698.
The percentage of people taking the test who are above 698 is ___%

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6 months 2021-08-05T00:55:39+00:00 1 Answers 12 views 0

2.5%

Step-by-step explanation:

The percentage of people taking the test who are above 698 is ___%

Empirical rule formula states:

95% of data falls within 2 standard deviations from the mean – between μ – 2σ and μ + 2σ .

99.7% of data falls within 3 standard deviations from the mean – between μ – 3σ and μ + 3σ

From the question, we have:

Mean of 514 and a Standard deviation of 92

Hence:

μ ± xσ

514 ± 92x = 698

514 + 92x = 698

92x = 698 – 514

92x = 184

x = 184/92

x = 2

Hence, the data is correct and it is 2 standard deviation from the mean. Therefore, 95% of data falls within 2 standard deviations from the mean – between μ – 2σ and μ + 2σ .

The question is asking us to find the percentage of people taking the test who are above 698 is calculated as:

100 – 95% /2

= 5/2

= 2.5%

The percentage of people taking the test who are above 698 is 2.5%