Question

suppose that iq scores have a bell-shaped distribution with a mean of 103 and a standard deviation of 14 . using the empirical rule, what percentage of iq scores are between 61 and 145 ?

Answer 1

Using the empirical rule for a bell-shaped distribution, approximately 99.7% of IQ scores fall between 61 and 145.

Step-by-step explanation:

The question is asking us to use the empirical rule to determine the percentage of IQ scores found between two given values. The empirical rule states that for a bell-shaped distribution, approximately 68% of data falls within one standard deviation of the mean, 95% within two standard deviations, and 99.7% within three standard deviations.

In this case, the mean IQ score is 103, and the standard deviation is 14. The requested range is between 61 and 145, which is three standard deviations below the mean (103 - 3*14 = 61) and three standard deviations above the mean (103 + 3*14 = 145). According to the empirical rule, this encompasses approximately 99.7% of the IQ scores.