Final answer:
The question requires listing possible samples when selecting two ages with replacement from given ages of 56, 46, and 60, determining the sample range for each, and calculating the probability of selecting each sample. With nine possible samples and three unique ages, the sample range varies, with the largest being 14 years and the smallest being 0 years. Each sample has an equal probability of 1/9.
Step-by-step explanation:
The question involves finding different possible samples, the sample range, and the probability of selecting two ages with replacement from the given ages of government officials (56, 46, and 60). Since selection is with replacement, the possible samples when selecting two ages are: (56, 56), (56, 46), (56, 60), (46, 56), (46, 46), (46, 60), (60, 56), (60, 46), and (60, 60).
The sample range is calculated as the difference between the maximum and minimum values within a sample. Since there are only three unique ages, it is straightforward to determine the range for each sample: for instance, the range for (56, 46) would be 56 - 46 = 10 years. The largest possible range is 60 - 46 = 14 years, and the smallest possible range is 0 years (when the same age is selected twice). To find the probability of any single event occurring, we need to consider all possible events. There are 3 possible ages to choose for the first selection and 3 possible ages for the second selection, making a total of 3 x 3 = 9 possible samples. As each age can be selected with equal probability, each sample has an equal chance of 1/9 or about 11.11% chance of being selected.