Scores of GRE are normally distributed with a mean of 505 and a standard deviation of 146. Use the 68-95-99.7 rule to find the percentage of people taking the test who score between 213 and 797.

Question

High School

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Answer :

adefunkeadewole adefunkeadewole · Answer 1 · 2025-01-26T07:47:51-05:00

Answer:

95%

Step-by-step explanation:

The 68-95-99.7 rule to find the percentage of people is also know as the empirical rule.

The empirical rule formula states that:

68% of data falls within 1standard deviations from the mean - between μ – σ and μ + σ .

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 question:

Mean (μ) = 505

Standard deviation (σ) = 146

Hence, we are to find the number of standard deviation which is represented as x

The score is between 213 and 797

μ - xσ

= 505 - 146x = 0

= 505 - 146x = 213

146x = 505 - 213

146x = 292

x = 292/146

x = 2

μ + xσ

505 +146x = 797

146x = 797 - 505

146x = 292

x = 292/146

x = 2

Hence, the percentage falls within 2 standard deviation from the mean.

Thus, from the formula above:

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

Therefore, the percentage of people taking the test who score between 213 and 797 is 95%