Answer
a) $P(1 \leq t \leq 5)= \approx 0.537$
b) $P(t\gt10) \approx 0.231$
Work Step by Step
We are given $f(t)=\frac{1}{(\ln20)t}$ for $t$ in $[1,20]$
a) $P(1 \leq t \leq 5)=\int^{5}_1\frac{1}{(\ln20)t}dt=\frac{\ln t}{\ln 20}|^5_1=\frac{\ln 5}{\ln 20} \approx 0.537$
b) $P(t\gt10)=\frac{1}{\ln 20}\int^{20}_{10}\frac{1}{t}dt=\frac{\ln t}{\ln 20} |^{20}_{10} \approx 0.231$
