\( 18(3.183 .2) \) 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 follo' (a) What percentage of people has an IQ score between 81 and 119 ? (b) What percentage of people has an IQ score less than 43 or greater than 157? (c) What percentage of people has an IQ score greater than 119 ? Pare: \( 76.67 \%, 15.33 \) of 20 poin (a) \( \square \% \) (Type an integer or a decimal.)

To determine the percentages using the empirical rule, we start with the given mean (100) and standard deviation (19). For part (a), the scores between 81 and 119 fall within the range of 1 standard deviation from the mean (100 - 19 = 81 and 100 + 19 = 119). According to the empirical rule, approximately 68% of the data falls within this range. So, \( \text{Percentage} = 68\% \). For part (b), we want to find the percentage of people with an IQ score less than 43 or greater than 157. These scores fall beyond 2 standard deviations from the mean (100 - 38 = 43 and 100 + 38 = 157). The empirical rule tells us that about 95% of the data falls between these scores, which means roughly 5% of the data is outside of this range. Therefore, the percentage for scores less than 43 or greater than 157 is \( 5\% \). For part (c), since the scores greater than 119 fall within the upper part of the distribution beyond 1 standard deviation, we know that 50% of the population is above the mean (100), and since 34% of the population lies between 100 and 119, we can calculate the score above 119. So the percentage greater than 119 is \( 50\% - 34\% = 16\% \). Putting it all together: - a) 68 - b) 5 - c) 16 Thus, for your answer: (a) \( 68 \% \) (b) \( 5 \% \) (c) \( 16 \% \)