Most production model hybrid cars use a large battery as the core component of their power system.The battery lifetime of a particular hybrid are follows an exponential distribution with a mean lifetime of 8.62 years.What is the probability that one of these hybrid cars will have a battery that will last between 8 and 10 years?
A) 0.3953
B) 0.0819
C) 0.6047
D) 0.1160

Question

Quizplus · Accepted Answer

We can use the exponential distribution formula: 
f(x) = λe^(-λx), for x ≥ 0 and λ > 0
where λ is the rate parameter, which is the inverse of the mean, in this case λ = 1/8.62 = 0.1159
To find the probability that the battery will last between 8 and 10 years, we need to calculate the following:
P(8 ≤ x ≤ 10) = ∫(from 8 to 10) λe^(-λx) dx
= (-e^(-λx)) (from 8 to 10)
= (-e^(-0.1159*10) + e^(-0.1159*8))
= 0.0819
Therefore, the probability that a hybrid car's battery will last between 8 and 10 years is 0.0819 or approximately 8.19%. The best choice is B.

Most Production Model Hybrid Cars Use a Large Battery as the Core