Question

IQs as measured by the Wechsler Adult Intelligence Scale are approximately Normally distributed with mean 100 and standard deviation 15. According to the 68-95-99.7 Rule, about _______ percent of adults will have IQs of at least 70.

Answer 1

According to the 68-95-99.7 Rule, about 97.5% of adults will have IQs of at least 70.

Step-by-step explanation:

IQ scores are generally distributed normally which indicates that they form a symmetric, bell-shaped curve when graphed, with most scores clustering around the middle. According to the 68-95-99.7 Rule, also known as the Empirical Rule, we know that approximately 68% of the values lie within one standard deviation of the mean, 95% within two standard deviations, and 99.7% within three standard deviations.

In the case of the Wechsler Adult Intelligence Scale, with a mean of 100 and a standard deviation of 15, an IQ score of 70 is two standard deviations below the mean. Using the Empirical Rule, we can determine that approximately 95% of adults' IQ scores will lie between 70 (100 - 2 * 15) and 130 (100 + 2 * 15). Therefore, to find the percentage of adults with IQs of at least 70, we look at the lower tail which accounts for 2.5% (100% - 97.5%) of the distribution lying beyond two standard deviations below the mean. Subtracting this from 100% gives us 97.5%, which is the percentage of adults who will have IQs of at least 70.