What % of the products has a shelf life of 5 days or more?

Question

Shelf life (in days) of a product is exponentially distributed. Further 22.31 % of these products have last 3 days or more. What % of the products has a shelf life of 5 days or more?

Answer 1

$$\int_{3}^{\infty} \lambda e^{-\lambda x} dx = 0.2231$$

$$e^{-3\lambda} = 0.2231$$

$$\lambda = -\frac{ln(0.2231)}{3}$$

$$\lambda = 0.5$$

$$P(X\ge 5) = \int_{5}^{\infty} 0.5 e^{-0.5 x} dx$$

$$ = e^{-5*0.5} = 0.08206=8.206\text{%}$$