Question

The lifetime X of an alkaline battery is exponentially distributed with λ = 0.025 per hour. the probabilities for the battery to last between 10 and 15 hours ? *

Answer 1

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

Given $\lambda=0.025$. Then

$$P(10<X\leq 15)=e^{-0.25(10)}-e^{-0.25(15)}\approx0.0915$$

The probability for the battery to last between 10 and 15 hours is 0.0915.