A group of 500 elders completed a test of cognitive functioning. the mean score was 85, the standard deviation was 5, and scores were normally distributed. approximately what percentage of the 500 scores fell between 80 and 90?

Question

Mathematics

Grace Fletcher

9 January, 16:03

A group of 500 elders completed a test of cognitive functioning. the mean score was 85, the standard deviation was 5, and scores were normally distributed. approximately what percentage of the 500 scores fell between 80 and 90?

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Answers (1)

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Braedon Hardy · Answer 1

By the Empricial Rule, approximately 68% of the 500 scores fell between 80 and 90

Step-by-step explanation:

The Empirical Rule states that, for a normally distributed random variable:

Approximately 68% of the measures are within 1 standard deviation of the mean.

Approximately 95% of the measures are within 2 standard deviation of the mean.

Approximately 99.7% of the measures are within 3 standard deviations of the mean.

In this problem, we have that:

Mean = 85

Standard deviation = 5

Approximately what percentage of the 500 scores fell between 80 and 90?

80 = 85 - 5

So 80 is one standard deviation below the mean

90 = 85 + 5

So 90 is one standard deviation above the mean

By the Empricial Rule, approximately 68% of the 500 scores fell between 80 and 90