Suppose that the lifespan of a piece of equipment is normally distributed with mean 10 years and standard deviation 3 years. A particular piece of equipment is now age 11 years. The firm is considering two options:

Replace it now

Wait until age 13 to replace it (unless it dies before then, in which case an unscheduled

replacement is necessary).

Suppose that immediate replacement will cost the company a. Replacement at age 13 - if the equipment lasts that long - will cost b, where b < a. An unscheduled replacement between now and age 13 - if the equipment dies suddenly during the next two years - will cost c, where c > a.

(a) What is the probability that, barring replacement now, the equipment will last until age 13?