Answer: 0.393 ; 0.9933
Step-by-step explanation:
Given that :
Mean lifetime follows an exponential distribution (m) = 6
a. What is the probability that the CPU fails in the next three years?
Using the poisson distribution formula :
1 - e^-λt
λ = 1/m = 1 / 6 = 0.1667
Probability of failure in next 3 years :
P(X < 3) = 1 - e^-λx
P(X < 3) = 1 - e^-0.1667*3
P(X < 3) = (1 - e^-0.5)
P(X < 3) = 1 - 0.6065306
P(X < 3) = 0.3934693
= 0.3935
b. Assume that your corporation has owned 10 CPUs for three years, and assume that the CPUs fail independently. What is the probability that at least one fails within the next three years?
Number of pc owned = 10
CPU failure is indepndent
Probability of atleast one fails :
1 - P(X ≥ 3)^n
P(X ≥ 3) = 1 - P(X < 3)
P(X ≥ 3) = 1 - 0.3935 = 0.607
Hence,
1 - P(X ≥ 3) = 1 - 0.6065^10
1 - P(X ≥ 3) = 1 - 0.0067345
1 - P(X ≥ 3) = 0.993265
= 0.9933
