Repairing pipelines Oil pipelines are made up of 30-foot segments. If a leak occ

Question

Repairing pipelines Oil pipelines are made up of 30-foot segments. If a leak occurs, the pipeline must be opened at a joint between segments to get access to make repairs.

1. What is the furthest distance from any leak to the nearest segment end?

2. Suppose leaks occur at random the length of the entire pipeline.   X is the distance from the next leak to the nearest segment end.   Give the probability density function of the random variable X.

3. What is the probability that the distance to the nearest segment end will be more than 9 feet?

4. There’s a 50% probability that the distance will be between 3 feet and _________________ feet?

Explanation / Answer

1) The leak at the middle of the pipe will be furthest from any end. So, the distance to any segment end from furthest leak = 30/2 = 15 feet

2) F(x) = X/15 for all X < 15, this is the probability density function

3) P(x >9) = 1 - P(x < 9)

= 1 - 9/15

= 2/5

4) P(K) - P(3) = 0.5

So, K/15 - 3/15 = 0.5

K - 3 = 7.5

K = 10.5

So, there is a 50% probability that the distance will be between 3 feet and 10.5 feet

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