Final answer:
Without specific data on the distribution of Emotional Health Index Scores, we cannot calculate the precise probability that a score is between 80.5 and 82.
Step-by-step explanation:
The question asks for the probability that a randomly selected occupation has an Emotional Health Index Score between 80.5 and 82. To find this probability, we need specific data about the distribution of the Emotional Health Index Scores across the different occupations. If we assume that the scores are evenly distributed or have a known distribution, we could apply the appropriate probability rules or statistical methods to calculate this probability. However, without the actual data or distribution, it's not possible to provide a specific number. If the data were normally distributed, we could use z-scores to find the probability within a certain range, but this information is not provided.