Answer to Question #205880 in Statistics and Probability for Lou Robert Cuyos

Question

The lifetime of an alkaline battery (measured in hours) is exponentially distributed with μ = 0.05. Find the probability a battery will last between 10 and 15 hours.

Answer 1

Let $X=$ the lifetime of a battery.

$$P(10\leq X\leq 15)=e^{-0.05(10)}-e^{-0.05(15)}$$

$$=e^{-0.5}-e^{-0.75}\approx0.134164$$

The probability a battery will last between 10 and 15 hours is $0.134164.$