Final answer:
The specific hours within which catastrophic failures must be repaired are not provided, but the statistical context given through the 30th and 75th percentiles indicates typical repair times. The 30th percentile is 2.25 hours (30 percent of repairs), and the 75th percentile is 3.375 hours (75 percent of repairs).
Step-by-step explanation:
The student's question pertains to the time frame within which catastrophic failures must be repaired. Utilizing the percentile concept in statistics, we can infer that the 30th percentile of repair times is 2.25 hours, which means 30 percent of repairs are completed in 2.25 hours or less. Furthermore, we also know that the 75th percentile is 3.375 hours, indicating that 75 percent of repairs are completed in 3.375 hours or less. While these statistics provide context, the specific timeframe within which catastrophic failures must be repaired is not specified and would typically depend on industry standards or service level agreements.
To solve similar problems, one may use equations like 0.75 k-1.5, obtained by dividing both sides by 0.4 to find the value of 'k' or adjust the equation by adding or subtracting from both sides to find the percentile thresholds in a set of data. For example, obtained by subtracting four from both sides: k = 3.375 helps us determine that the longest 25 percent of furnace repairs take at least 3.375 hours.