A psychologist wants to estimate the proportion of people in a population with IQ scores between 80 and 140. The IQ scores of th

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A psychologist wants to estimate the proportion of people in a population with IQ scores between 80 and 140. The IQ scores of th

is population are normally distributed with a mean of 110 and a standard deviation of 15. Use the Empirical Rule to estimate the proportion.

Mathematics

1 answer:

ryzh [129] · Answer 1 · 2023-09-06T16:59:34+03:00

Using the Empirical Rule, it is found that the proportion of people in a population with IQ scores between 80 and 140 is of 0.95 = 95%.

<h3>What does the Empirical Rule state?</h3>

It 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 deviations of the mean.

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

Considering the mean of 110 and the standard deviation of 15, we have that:

80 = 110 - 2 x 15.

140 = 110 + 2 x 15.

These values are both the most extreme within 2 standard deviations of the mean, hence the proportion of people in a population with IQ scores between 80 and 140 is of 0.95 = 95%.

More can be learned about the Empirical Rule at brainly.com/question/24537145

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