Final answer:
The questions pertain to the calculation of probabilities and percentiles for sample means in a normally distributed population. Specific calculations require additional information such as sample size and population standard deviation, which are not provided. Hence, only the methodology of how such problems are solved can be described, not the actual numerical solutions.
Step-by-step explanation:
To address the statistics problems presented, it's important to note that all questions revolve around the concept of sample means and their probabilities within a normally distributed population.
(a) To find the probability that the sample mean rent is greater than $2654, we would normally use the z-score formula. However, to calculate the z-score and the corresponding probability, we need additional information such as the sample size and the population standard deviation or the standard error. Without this information, we cannot provide a numerical answer.
(b) Similar to part (a), computing the probability that the sample mean rent is between $2400 and $2600 requires the sample size and the population standard deviation. Again, without these details, we are unable to calculate the probability.
(c) To find the 45th percentile of the sample mean, we would use a normal distribution table or software, but we also need the sample size and population standard deviation to proceed
(d) Determining whether a sample mean greater than $2695 is unusual involves calculating its z-score and corresponding probability. The threshold for 'unusual' is typically a probability lower than 5%, but we need additional data to perform this calculation.
(e) An individual apartment having rent greater than $2695 could be considered unusual if it falls significantly outside the range of typical rent prices (e.g., more than two standard deviations from the mean). However, 'unusual' is context-dependent and may vary based on location, market conditions, and amenities provided.
For the problems that involve calculating specific probabilities, percentiles, and determining unusualness, these tasks are standard in statistics when given the appropriate data points including sample size and standard deviation. Without them, we can only describe the methodological steps needed to solve such problems.