solution

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 20 months. Assume product life can be described by an exponential distribution T / MTBF e-T / MTBF T/MTBF e-T / MTBF T/MTBF e-T/MTBF 8.10 0.9048 2.60 0.0743 0.20 5.10 0.0061 0.8187 2.70 0.0672 8.30 5.28 0.0055 0.7408 2.80 0.0608 5.30 0.40 0.0050 0.6703 2.90 0.8550 5.40 0.0045 8.50 0.6065 3.00 0.0498 5.50 8.8841 0.60 0.5488 3.10 0.0450 0.70 5.60 0.8037 0.4966 3.20 0.0488 5.70 0.80 0.0033 0.4493 3.30 0.0369 8.90 5.80 0.0030 0.4066 3.40 0.0334 5.90 1.00 0.0027 0.3679 3.50 0.0302 6.00 0.0025 1.10 0.3329 3.60 0.0273 6.10 8.0022 1.20 0.3012 3.70 0.0247 6.28 0.0020 1.30 0.2725 3.80 0.0224 6.30 0.0018 1.40 0.2466 3.90 0.0202 6.40 9.2017 1.50 0.2231 4.00 0.0183 6.50 8.2015 1.68 @.2019 4.18 0.0166 6.60 8.8814 1.70 0.1827 4.20 0.015€ 6.70 8.2012 1.80 0.1653 4.30 0.0136 6.80 0.0011 1.90 0.1496 4.40 0.0123 6.90 0.0010 2.00 0.1353 4.59 0.0111 7.00 0.0889 2.10 0.1255 4.60 0.0101 2.20 0.1108 4.70 0.0091 2.30 0.1003 4.80 0.0082 2.40 0.0907 4.90 0.0074 2.50 0.0021 5.00 0.0067 a. If service contracts are offered for the expected life of the calculator, what percentage of those sold would be expected to fall during the service period? (Round your answer to 4 decimal places.) 1.90 2.00 2.10 6.80 6.90 7.00 0.0811 0.0010 0.0009 2.20 0.1496 0.1353 0.1255 0.1108 0.1003 9.9907 0.9821 4.30 4.40 4.50 4.60 4.70 4.80 4.90 5.00 0.0136 0.0123 0.0111 0.0101 0.0091 0.0082 0.0074 0.0067 2.30 2.40 2.50 a. If service contracts are offered for the expected life of the calculator, what percentage of those sold would be expected to fall during the service period? (Round your answer to 4 decimal places.) 1–TMTBF b. What service period would result in a failure rate of approximately 30 percent? (Round intermediate calculations to 2 decimal places and final answer to the nearest whole number.) months