Question

A psychologist wants to estimate the proportion of people in a population with IQ scores between 80 and 140. The IQ scores of this population are normally distributed with a mean of 110 and a standard deviation of 15. Use the Empirical Rule to estimate the proportion.

Answer 1

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%.

What does the Empirical Rule state?

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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