Exam P Practice Problem 4

Problem 4a
Suppose that the lifetime of an electronic device follows an exponential distribution. The device is sold with a t-year warranty. The manufacturer estimated that at the expiration of the warranty, about 85% of the devices are still working. The manufacturer is considering offering an extended warranty for an additional t years. What proportion of all devices that are found to be working at the expiration of the regular warranty will be working at the end of the extended warranty?

Problem 4b
Suppose that the lifetime of an electronic device follows an exponential distribution. The device is sold with a t-year warranty. The manufacturer estimated that at the expiration of the warranty, about 80% of the devices are still working. The manufacturer is considering offering an extended warranty for an additional \displaystyle \frac{t}{2} years. What proportion of all devices that are found to be working at the expiration of the regular warranty will be working at the end of the extended warranty?

Solution is found below.

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Solution to Problem 4a
0.85. Hint: the exponential distribution is memoryless.

Answer to Problem 4b
0.894427191.

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