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Alinara [238K]
3 years ago
11

The waiting time at an elevator is uniformly distributed between 30 and 200 seconds. what is the probability a rider must wait m

ore than 1.5 minutes?
Mathematics
1 answer:
stira [4]3 years ago
5 0
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
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