Probabilit y of a valve falling in a time period

[estado3]

Homework Statement

A large population of nominally identical "fail to close" control valves are put into service on the same day on similar installations. The number of valve failures per month N was recorded over time and shown to be given approximately by the following equation

Calculate the probability that the valve fails in the time period (0,24) months

Homework Equations

N = 0.001 X t^1.26 (failures/month)

The Attempt at a Solution

have tried it with the density function and the cumulative distribution function with N being lambda but still far away from the ans of 0.4414

The second part of the question also has be stumped as it states if the installation contains 3 valves in unrelated parts of the plant, calculate the probability that the installation is free of valve failure over the same time period (ans is 0.1743)

 

[HallsofIvy]

Homework Statement

A large population of nominally identical "fail to close" control valves are put into service on the same day on similar installations. The number of valve failures per month N was recorded over time and shown to be given approximately by the following equation

Homework Equations

N = 0.001 X t^1.26 (failures/month)

The Attempt at a Solution

have tried it with the density function and the cumulative distribution function with N being lambda but still far away from the ans of 0.4414

What was the question that 0.4414 is the answer to? I see no question given here!

The second part of the question also has be stumped as it states if the installation contains 3 valves in unrelated parts of the plant, calculate the probability that the installation is free of valve failure over the same time period (ans is 0.1743)

What time period?

 

[estado3]

edited