Question

The amount of time it takes Isabella to wait for the bus is continuous and uniformly distributed between 3 minutes and 17 minutes. What is the probability that it takes Isabella more than 5 minutes to wait for the bus

Answer 1

P(X>5) = 0.857

Explanation:

Let X
`\sim` uniform(3.17)

`f(x) = (1)/(17-3) ; \ \ \ 3 \le x \le 17`

The required probability that it will take Isabella more than 5 minutes to wait for the bus can be computed as:

`P(X > 5) = \int ^(17)_(5) f(x) \ dx`

`P(X > 5) = \int ^(17)_(5) (1)/(17-3) \ dx`

`P(X > 5) =(1)/(14) \Big [x \Big ] ^(17)_(5)`

`P(X > 5) =(1)/(14) [17-5]`

`P(X > 5) =(12)/(14)`

P(X>5) = 0.857