The mean life of a certain computer hard disk in continual use is 4 years. How l

Question

The mean life of a certain computer hard disk in continual use is 4 years.

How long a warranty should be offered if the vendor wants to ensure that not more than 39 percent of the hard disks will fail within the warranty period? (Round your intermediate values to 4 decimal places and final answer to 4 decimal places.)

How long a warranty should be offered if the vendor wants to ensure that not more than 22 percent of the hard disks will fail within the warranty period? (Round your intermediate values to 4 decimal places and final answer to 4 decimal places.)

The mean life of a certain computer hard disk in continual use is 4 years.

Explanation / Answer

Solution:

Let X be the event of the length of the warranty.
From the given information, = 4 years.
The exponential distribution mean is: 1/ = 1/4 = 0.25

a) The warranty offered if the vendor wants to ensure that not more than 39% is,
P(X x) = 39%
1- e^-(1/)x = 0.39
e^-(1/)x = 1-0.39
e^-(0.25)x = 0.61
-0.25x = ln(0.61)
-0.25x = -0.4942
x = 0.4942/0.25
= 1.9768
Hence, the required warranty period is : 1.9768 years.

b) The warranty offered if the vendor wants to ensure that not more than 22% is,
P(X x) = 22%
1- e^-(1/)x = 0.22
e^-(1/)x = 1-0.22
e^-(0.25)x = 0.78
-0.25x = ln(0.78)
-0.25x = -0.2485
x = 0.2485/0.25
= 0.994
Hence, the required warranty period is : 0.994 years.

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