Question

Suppose that a failure can occur at any point of an electricity line of 10 kilometers (1km = 1000m).

(a) (5 points) What is the probability that the failure will occur on the first 500 meters?

(b) (5 points) What is the median value of the point where the failure occurs?

(c) (10 points) The cost to repair this network depends on the distance from the service station to where the failure occurred.

Consider that the service station is at the origin of the line and that the cost is $200 for distances of up to 3 kilometers,

$400 for distances between 3 and 8, and $1000 for distances over 8 kilometers.

The cost function C(x) (in dollars) is shown below, where x is the distance from the service station to where the failure occurred.

What is the average cost of the repair?

C(x) = { 200, 0 ≤ x ≤ 3000

400, 300 < x ≤ 8000

1000, 8000 < x ≤ 10000

0, otherwise}

Answer 1