A manufacturer of programmable calculators is attempting to determine a reasonable free- service period for a model it will introduce shortly. The manager of product testing has indicated that the calculators have an expected life of 30 months. Assume product life can be described by an exponential distribution. a. If service contracts are offered for the expected life of the calculator, what percentage of those sold would be expected to fail during the service period?
b. What service period would result in a failure rate of approximately 10 percent?

a. P(failure before T) = 1 - e^(-(T/MTBF))(1)

Where e = value obtained from table, T = Length of service before failure, MTBF = 30, Mean time before failure = 30 months

P = 1 - e^(-(T/MTBF))

P = 1 - e^(-(30/30))

P = 1 - 0.3679

P = 0.6321

So, 63.21% of sold product would all during the service period if service contracts are offered for expected life of the calculator

b. Here, the value of P is given. P = 10% = 0.10

1 - e^(-(T/MTBF)) = 0.10

e^(-(T/30) = 0.90

T/30 = 0.10

T = 0.10*30

T = 3 months

So, the service period would be 3 month that result in failure rate of 10%

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