2. (10pt) The initial cost of a machine is 3. The lifetime of the machine has an exponential dist...
2. (10pt) The initial cost of a machine is 3. The lifetime of the machine has an exponential distribution with a mean of 3 years. The manufacturer is considering offering the following warranty. - if the machine fails within 1 year, the full purchase price is refunded. if the machine fails after 1 year but before 2 years, 3/4 of the purchase price is refunded. price is refunded, an<d What is the expected warranty payment? if the machine failed after...
The lifetime of a particular brand of television follows the exponential distribution and has an average lifetime of 7 years. If the manufacturer provided a warranty that replaces any television that fails within one year, what proportion of televisions will the manufacturer need to replace?
A machine has three components that are identical and they operate independently of each other. The machine will operate as long as any one of three of the components is operating, The lifetime of each component follows an exponential distribution with a mean lifetime of 2 years. Determine the probability the machine is still operating after 1.5 years. Suppose the machine in the previous problem requires all three of the components to operate. If the lifetime of each component follows...
The lifetime, in years, of a gearbox operating continuously has a Weibull distribution with λ = 0.1 and k = 2. The purchase price of the gearbox is $1000. The manufacturer warranties the gearbox of (a) refunding the entire purchase price if the gearbox fails during its first year of operation, and (b) refunding 40% of the purchase price if the gearbox fails during its second year of operation. What is the expected refund amount per gearbox?
The lifetime of a printer costing 200 is exponentially distributed with mean 2 years. The manufacturer agrees to pay a full refund to a buyer if the printer fails during the first year following its purchase, and a one-half refund if it fails during the second year. If the manufacturer sells 100 printers, how much should it expect to pay in refunds? A. 6,321 B. 7,358 C. 7,869 D. 10,256 E. 12,642
The time until failure for an electronic switch has an exponential distribution with an average time to failure of 4 years, so that λ = 1/4 = 0.25. (Round your answers to four decimal places.) (a)What is the probability that this type of switch fails before year 3? (b)What is the probability that this type of switch will fail after 5 years? (c) If two such switches are used in an appliance, what is the probability that neither switch fails...
Machine “A” has 3 components with independent exponential lifetimes (means= 2, 3 & 5 years). The machine functions if & only if all 3components function. Machine “B” has 2 components with independent exponential lifetimes (means= 5 & 7years). This machine operates if& only if both components function. Determine the probability that, in machine A, the component with the lowest expected lifetime outlasts both of the other components. (a) 0.1482. (b) 0.1696. (c) 0.2134. (d) 0.2387. (e) 0.2516
1. Suppose that the longevity of a light bulb is exponential with a mean lifetime of eight years. Find the probability that a light bulb lasts between 6 and 8 years. a. 0.875 b. 0.125 c. 0.896 d. 0.104 2. At a 911 call center, calls come in at an average rate of one call every two minutes. Assume that the time that elapses from one call to the next has the exponential distribution. Find the probability after a call is...
A light bulb (the lifetime is assumed to follow an exponential distribution) has a mean life of 400 hours. What is the probability of the bulb lasting 1) less than 300 hours; 2) more than 500 hours; 3) between 200 and 500 hours?
Assume that you work at Apple and have determined based on previous sales data that the Mac computers last a mean of 10 years and approximately follow an exponential distribution. Each computer costs the company $200 dollars to manufacture. If you are tasked with determining how much a 4-year full replacement warranty on a broken computer should cost customers, what is the lowest price the company should offer for that replacement warranty to have an expected return of $0? If...