Final answer:
The student's question relates to statistics within mathematics, dealing with analysis and interpretation of hospital stay data, including average lengths and costs, and understanding sampling distributions and percentiles.
Step-by-step explanation:
The question involves interpreting data, calculating averages, understanding standard deviations, and making inferences about population characteristics based on sample data. This falls under the subject of statistics, a branch of mathematics. Specifically, the student is dealing with concepts like the mean length of hospital stay, the likelihood of events based on the distribution of data, and interpreting percentiles. In case (a) for example, 'X' would typically refer to the average length of stay for the sample of women surveyed.
Regarding question (i), if an individual stayed more than five days in the hospital, this could be considered less likely if the mean is significantly lower than five. For question (ii), whether it is likely that the average stay of 80 women was more than five days can be assessed using the central limit theorem and knowledge of the sample mean and standard deviation. In the scenario of a 90-minute wait being in the 82nd percentile, this indicates that the individual's wait time is longer than 82 percent of all wait times, which can be interpreted as a negative experience compared to most other patients.