give an example of the type of situation where this statistic might be critical to making good decisions about

Question

An example where standard deviation might be critical to making good decisions about the population

Answer 1

Finance:
Standard deviation might be used to characterize how much spread to expect in a group of investments. High standard deviation implies high uncertainty.

Manufacturing:
Likewise for manufactured parts. High standard deviation here means highly variable parts. Manufacturers was low variability, so that parts fit together well.

Medicine:
A drug might be tested and shown to reduce blood pressure. If the amount of reduction has a high standard deviation, though, the drug may not be reliable.

Answer 2

Insurance companies would be very interested in the standard deviation of life expectancy of heavy smokers.from the pop norm.

For money reasons.

Will

Answer 3

Investing in the stock market.
listening to ads for "9 out of 10 doctors recommend..."

Stats are a good way to evaluate the possibilities for successfully reaching a goal.