Question

1. The first year you obtain your Professional Engineer seal, you design and observe construction of small dams, each of which is in a different area of the country. Each of these dams is designed to pass the 200-year storm without overtopping, since they are relatively small and no loss of life or damage to property is likely if they do fail. After that first year, you never design another dam for the rest of your career since you move into management. a. What is the probability that the very first dam you designed will overtop during your anticipated 45-year career

Answer 1

The probability that the very first dam you designed will overtop during your anticipated 45-year career is 0.7985.

Explanation:

The question is related to the reliability function.

The reliability of the dam built follows an Exponential distribution with mean time between failure as 200 years.

Then the parameter of the exponential distribution will be:

`\lambda=(1)/(200)=0.005`

The reliability function for the time in which the dam will overtop is given by:

`R(t)=e^(-\lambda t)`

Compute the probability that the very first dam you designed will overtop during your anticipated 45-year career as follows:

`R(t)=e^(-\lambda t)`

`R(45)=e^(-0.005* 45)`

`=e^(-0.225)\\=0.7985`

Thus, the probability that the very first dam you designed will overtop during your anticipated 45-year career is 0.7985.