Final answer:
Using the empirical rule for a bell-shaped distribution with a mean of 100 and a standard deviation of 18: (a) About 95% of people have an IQ score between 64 and 136, (b) 16% have an IQ score less than 82 or greater than 118, and (c) Less than 0.5% have an IQ score greater than 154.
Step-by-step explanation:
The question asks about the use of the empirical rule, also known as the 68-95-99.7 rule, to determine certain probabilities related to IQ scores. Since IQ scores have a bell-shaped distribution with a mean of 100 and a standard deviation of 18, we can apply this rule to find the requested percentages.
- Percentage of people with an IQ score between 64 and 136: 64 is two standard deviations below the mean (100 - 2*18) and 136 is two standard deviations above the mean (100 + 2*18). According to the empirical rule, approximately 95% of the data is within two standard deviations of the mean. Therefore, about 95% of people have an IQ score between 64 and 136.
- Percentage of people with an IQ score less than 82 or greater than 118: 82 is one standard deviation below the mean (100 - 18) and 118 is one standard deviation above the mean (100 + 18). Since 68% of people are within one standard deviation of the mean, 100% - 68% = 32% are outside this range. However, since this range is split equally on both sides of the mean, each tail will have half of 32%, which is 16%. Therefore, 16% of people have an IQ score less than 82 or greater than 118.
- Percentage of people with an IQ score greater than 154: 154 is three standard deviations above the mean (100 + 3*18). According to the empirical rule, more than 99% of the data is within three standard deviations of the mean. Therefore, less than 1% of people have an IQ score greater than 154, and since half of that would be represented in the upper tail, it is less than 0.5%.