Mechanical engineers at Purdue University conducted a reliability analysis of lead-free solder joints used in microscopic electronic packages (Electronic Components and Technology Conference, May 2005). The minimum time required by cracks in the solder joints to propagate through the weakest joint (i.e., the failure time) was approximated using a Weibull distribution with parameters α and β. The researchers estimated the shape parameter α = 3.5 and the mean failure time μ = 2,370 hours.

a. Use these estimates and your knowledge of the Weibull distribution to find an estimate of the scale parameter β. 

b. Give an expression for the hazard rate of the failure time distribution.

c. Find the hazard rate at t = 5,000 hours.