Question

The cycle time for trucks hauling concrete to a highway construction site is uniformly distributed over the interval 50 to 70 minutes. What is the conditional probability that the cycle time is no more than 65 minutes if it is known that the cycle time exceeds 55 minutes?

Answer 1

2/3=0.6667

Explanation:

Let X be the cycle time for trucks hauling concrete to a highway construction site

Given that X is U(50,70)

Hence pdf of X is

`f(x) = (1)/(20) ,50<x<70`

Let A be the event that cycle time is no more than 65 minutes and

B the event cycle time exceeds 55 minutes

Required probability

= the conditional probability that the cycle time is no more than 65 minutes if it is known that the cycle time exceeds 55 minutes

= P(A/B)

=
`(P(A\bigcapB))/(P(B)) \\=(P(55<x<65))/(P(X>55)) \\=(65-55)/(70-55) \\=(2)/(3)`