To investigate the performance of the central processing unit (CPU) of a certain type of microcomputer, 20 CPUs were placed on test for a period of 5,000 hours. When the test was terminated, four CPUs had failed with failure times of 1,850, 2,090, 3,440, and 3,970 hours. Assume a negative exponential failure time distribution.

a. Find a 90% confidence interval for the mean time β until failure of the microcomputer’s CPU.

b. Find a 90% confidence interval for the reliability of the CPU at time t = 2,000 hours.

c. Find a 90% confidence interval for the hazard rate of the CPU.