\( 1 \leftarrow \quad \) Scores of an IQ test have a bell-shaped distribution with a mean of 100 and a standard deviation of 19. Use the empirical rule to determine the following. (a) What percentage of people has an IQ score between 81 and 119 ? (b) What percentage of people has an IQ score less than 62 or greater than 138 ? (c) What percentage of people has an IQ score greater than 157 ? (a) \( 68 \% \) (Type an integer or a decimal.) (b) \( \square \% \) (Type an integer or a decimal.)

Using the empirical rule, which states that in a normal distribution: - Approximately 68% of the data falls within one standard deviation (±1σ) of the mean. - About 95% falls within two standard deviations (±2σ). - Roughly 99.7% falls within three standard deviations (±3σ). Given a mean (µ) of 100 and a standard deviation (σ) of 19: (a) IQ scores between 81 and 119 correspond to one standard deviation from the mean (100 - 19 = 81 and 100 + 19 = 119), so the percentage is \( 68\% \). (b) To find the percentage of people with IQ scores less than 62 or greater than 138, we need to determine the boundaries. IQ scores below 62 (100 - 2*19 = 62) correspond to about 2.5% (from the lower tail of the distribution). Similarly, scores above 138 (100 + 2*19 = 138) also corresponds to about 2.5% (from the upper tail). Thus, the total percentage for scores less than 62 or greater than 138 is \( 2.5\% + 2.5\% = 5\% \). (c) For scores greater than 157, which is beyond three standard deviations (100 + 3*19 = 157), the empirical rule indicates that only about 0.15% of people have an IQ above this score. So, to recap: (b) \( 5\% \) (c) \( 0.15\% \)