What is the practical application of the relationship between the expected value and the standard deviation of a normal distribution?

What is the practical application of the relationship between the expected value and the standard deviation of a normal distribution?

• A. Identifying whether a loss exposure is high-frequency and low-severity, or high-severity and low frequency
• B. Determining a maintenance schedule for equipment that could become dangerous if it were to fail
• C. Selecting which risk management technique would be most appropriate for a particular loss exposure
• D. Predicting when losses, such as physical damages losses to an automobile fleet, are likely to occur

Answer: (B)

The practical use of the mean and variability in a normal distribution is to time preventive actions so the risk of a failure is kept acceptably low. If time-to-failure is modeled as approximately normal, the mean tells you the typical or expected time before a failure, while the standard deviation tells you how much actual failure times vary around that average. With those two parameters, you can calculate the probability that a component will fail before a planned maintenance interval. By choosing maintenance timing that keeps this probability low, you reduce the chance of a dangerous failure. This approach directly uses the mean–variability relationship to schedule maintenance, rather than making broad classifications of exposure, selecting a risk-management technique, or merely predicting when losses will occur.

The practical use of the mean and variability in a normal distribution is to time preventive actions so the risk of a failure is kept acceptably low. If time-to-failure is modeled as approximately normal, the mean tells you the typical or expected time before a failure, while the standard deviation tells you how much actual failure times vary around that average. With those two parameters, you can calculate the probability that a component will fail before a planned maintenance interval. By choosing maintenance timing that keeps this probability low, you reduce the chance of a dangerous failure.

This approach directly uses the mean–variability relationship to schedule maintenance, rather than making broad classifications of exposure, selecting a risk-management technique, or merely predicting when losses will occur.