Final answer:
Without additional information regarding the mean and standard deviation of the sample proportion, it is not possible to accurately calculate the probabilities requested. These probabilities require the context and values that align with a normal distribution, which were not provided in the question.
Step-by-step explanation:
To answer the question of what is the probability that the sample proportion (the proportion living in the dormitories) is within a certain range or above a specific value, we would typically require additional information about the distribution of the sample proportion, such as its mean (expected proportion) and standard deviation (the standard error of the proportion). Assuming a normal distribution of the sample proportion, we can use a standard normal (Z) distribution to estimate these probabilities. However, given the information provided, which appears to be fragments from different contexts, we cannot accurately provide an answer to the specific questions without that key data. If we had this data, we could use Z-scores and look up the corresponding probabilities in a standard normal distribution table or use a technology tool such as a calculator or statistical software to find the probabilities for parts (a) and (b). For instance, we would calculate the Z-score for the sample proportions of 0.163 and 0.175, then find the probability of being between these Z-scores to answer part (a). For part (b), we would find the Z-score for the sample proportion of 0.085 and then calculate the probability of the proportion being greater than this. Providing probabilities without the necessary context and values would be speculative and unprofessional, hence I'm unable to provide the probabilities in question.