Question

The lung cancer hazard rate$\lambda \left(t\right)$of a $t$-year-old male smoker is such that

$\lambda \left(t\right)=.027+.00025{(t-40)}^2$$t\ge 40$

Assuming that a $40$-year-old male smoker survives all other hazards, what is the probability that he survives to

$\left(a\right)$age$50$and $\left(b\right)$age 60 without contracting lung cancer?

Short answer

$t=50\Rightarrow \lambda \left(50\right)=0.052$

$t=60\Rightarrow \lambda \left(60\right)=0.127$

Step-by-step solution

Given Information.

$\lambda \left(t\right)=.027+.00025{(t-40)}^{2}t\ge 40$

Part a Step 2 Explanation.

$t=50,$

$\lambda \left(50\right)=0.027+0.00025{(50-40)}^2$

$$\begin{gathered} =0.027+0.025 \\ =0.052 \end{gathered}$$

Part b Step 3 Explanation.

$$\begin{gathered} t=60, \\ \lambda \left(60\right)=0.0027+0.000259{(60-40)}^2 \end{gathered}$$

=0.127