A wet-mix, steel-fiber-reinforced microsilica concrete (called shotcrete), used extensively in Scandinavia, is now being marketed in the United States. The material is said to have a minimum 28-day breaking strength of 9,000 pounds per square inch (psi) of compression. To investigate the breaking strength of the new product, seven pieces of shotcrete were subjected to 9,000 psi of compression daily until they failed. The times to failure were 33, 35, 61, 38, 21, 41, and 52 days. Assume that the shotcrete has an exponential failure time distribution when subjected to 9,000 psi of compression.

a. Find a 90% confidence interval for the mean time β until the shotcrete fails.

b. Find a 90% confidence interval for the probability that the shotcrete will not fail before the 28-day specified minimum.

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