Engineers are developing a new type of insulation. They want to determine the sample sizes necessary to estimate the 10th percentile when the distance from the lower bound to the estimate is within 100, 200, or 300 hours. The engineers will perform reliability tests on small specimens for 1000 hours. They use the following information for the test plan:
- Approximately 12% of the specimens are expected to fail in the first 500 hours of the test.
- Approximately 20% of the specimens are expected to fail by the end of 1000 hours.
- The failure times for the insulation follow a Weibull distribution.