Needing help with my homework. There are a total of three short questions, 1) A

Question

Needing help with my homework. There are a total of three short questions, 1) A DVD Burner has a mean time between failures of 79 weeks. Find the probability that the unit will last at least 90 weeks. ------- 2) A DVD Burner has a mean time between failures of 81 weeks. Find the probability that the unit will fail between 61 and 89 weeks in other words, find P (61 < t < 89) -------- 3) The useful life of an artificial heart valve is normally distributed with a mean of 47 months and a standard deviation of 2 months. Determine the probability that the valve will last at least 45 month(s), before wearing out. (Find P( X > 45 ).

Explanation / Answer

1. mean time between failures = 79 weeks

Time = 90 weeks

Reliability = e^(-time/mean time between failures) =  e^(-90/79)= 0.3201

Probability that it will last for atleast 90 weeks = 0.3201

2. Mean time between failures = 81 weeks

P(61<t<89) = 1-( e^(-61/81) - e^(-89/81) ) = 1 - (0.4709 - 0.333) =1- 0.1379 = 0.8621

3. mean time = 47
standard deviation = 2

Probabilty that it will last for atleast 45 months = P(x>45)

z = (45-47)/2 = -1
P(z>-1) = 0.841345

P(X>45) = 0.841345

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