PLEASE SHOW ALL WORKSolutionSolution a 1 43 e t MTBF e 4

PLEASE SHOW ALL WORK!

Solution :

a) (1) 43 = e ^{-t / MTBF}

= e ^{-43 / 29}

P(43) = 0.2275

P(53) = e^-53/29

53 = 0.1608

63 = e ^-63/29

P(63) = 0.1144

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b) The probability that the unit will fail by 31 months is first calculated and the the probability that it will fail sooner than 31 months is found

P(31) = e^-31/29

P(31) = 0.3433

P(<31) = 1 - 0.3433

P(<31) =0.6566

P(18) = e^-18/29

P(18)= 0.5376

P(<18)= 0.4623

P(8) =e^-8/29

P(8) = 0.7589

P(<8) = 0.2410