### 8.1 Assigning a Measure to Likelihood

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• Math Help

Here are some observations about the world life expectancies shown in the map on page 357 (also shown below) and countries with populations of 13 million or more.

• Australia, Canada, France, Italy, and Spain have life expectancies over 80 years.
• Afghanistan, Angola, Mozambique, Nigeria, and South Africa have life expectancies under 50 years.
• Of the three most populous countries in North America, Canada has the highest life expectancy (81.3), followed by the United States (78.2), and Mexico (76.3).

• Consumer Suggestion

The current U.S. life expectancy is 77.9 years. Life expectancies vary by geographical location, gender, race, and history of disease. To find out more about life expectancy around the world, visit the World Health Organization.

• Checkpoint Solution
1. The graph shows that as age increases, the years of life remaining decreases. The decrease appears to be almost linear until the age of 60 or 70 when it flattens out and approaches zero. The graph also shows that males have fewer years of life remaining than females at every age.
2. Given the age and gender of a person applying for insurance, an actuary would use this graph to find the number of years of life remaining for the person. Then the actuary would calculate an annual or monthly premium so that the amount the person pays into the policy would accumulate to at least enough to pay the benefit at the time the person is expected to die.
3. Yes, the graph seems reasonable. It makes sense that as a person gets older, the number of years of life remaining decreases. When the graph is approximately linear, the slope is about -1. This is reasonable because after living one more year, you should expect to have one less year remaining. It is also reasonable that eventually the graph flattens out. If it continued to decrease linearly, it would become negative.

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