Question

The waiting time at an elevator is uniformly distributed between 30 and 200 seconds. what is the probability a rider must wait more than 1.5 minutes?

Answer 1

1.5 minutes = 90 second

The probability density function is

$f_X(x)=\begin{cases}\dfrac1{200-30}=\dfrac1{170}&\text{for }30\le x\le200\\\\0&\text{otherwise}\end{cases}$

so the probability of interest is

$\mathbb P(X>90)=\displaystyle\int_{90}^\infty f_X(x)\,\mathrm dx$
$\mathbb P(X>90)=\dfrac1{170}\displaystyle\int_{90}^{200}\mathrm dx$
$\mathbb P(X>90)=\dfrac{200-90}{170}=\dfrac{11}{17}\approx0.6471$