Suppose that the lifespan of a piece of equipment is normally distributed with mean 10 years and standard deviation of 3 years. A particular piece of equipment's current age is 11 years. The firm is considering two options; i) replace it now, ii) 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 TL. Replacement at age 13 (if the equip- ment lasts that long) will cost b TL, where b < a. An unscheduled replacement between now and age 13 (that is, if the equipment dies suddenly during the next two years) will cost c TL, where c > a. • What is the probability that, barring replacement now, the equipment will last until age 13? 2 • What is the expected cost of replacement if the equipment is not replaced now? • Under what condition a, b and c, is expected cost lower if equipment is replaced now, rather than under the age 13 policy?
Suppose that the lifespan of a piece of equipment is normally distributed with mean 10 years and standard deviation of 3 years. A particular piece of equipment's current age is 11 years. The firm is considering two options; i) replace it now, ii) 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 TL. Replacement at age 13 (if the equip- ment lasts that long) will cost b TL, where b < a. An unscheduled replacement between now and age 13 (that is, if the equipment dies suddenly during the next two years) will cost c TL, where c > a. • What is the probability that, barring replacement now, the equipment will last until age 13? 2 • What is the expected cost of replacement if the equipment is not replaced now? • Under what condition a, b and c, is expected cost lower if equipment is replaced now, rather than under the age 13 policy?
A First Course in Probability (10th Edition)
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![Suppose that the lifespan of a piece of equipment is normally distributed with mean 10 years and standard
deviation of 3 years. A particular piece of equipment's current age is 11 years. The firm is considering
two options; i) replace it now, ii) 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 TL. Replacement at age 13 (if the equip-
ment lasts that long) will cost b TL, where b < a. An unscheduled replacement between now and age 13
(that is, if the equipment dies suddenly during the next two years) will cost c TL, where c > a.
• What is the probability that, barring replacement now, the equipment will last until age 13?
• What is the expected cost of replacement if the equipment is not replaced now?
• Under what condition a, b and c, is expected cost lower if equipment is replaced now, rather than
under the age 13 policy?
2.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F53c8537d-fbce-4254-817d-a44f730821eb%2Ffec9ecc4-c065-418c-8708-69366e287c47%2Fodiitfh_processed.png&w=3840&q=75)
Transcribed Image Text:Suppose that the lifespan of a piece of equipment is normally distributed with mean 10 years and standard
deviation of 3 years. A particular piece of equipment's current age is 11 years. The firm is considering
two options; i) replace it now, ii) 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 TL. Replacement at age 13 (if the equip-
ment lasts that long) will cost b TL, where b < a. An unscheduled replacement between now and age 13
(that is, if the equipment dies suddenly during the next two years) will cost c TL, where c > a.
• What is the probability that, barring replacement now, the equipment will last until age 13?
• What is the expected cost of replacement if the equipment is not replaced now?
• Under what condition a, b and c, is expected cost lower if equipment is replaced now, rather than
under the age 13 policy?
2.
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