1. Copyright © 2009 Pearson Education, Inc. 6.4 Ideas of Risk and Life Expectancy LEARNING GOAL Compute and interpret various measures of risk as they apply to travel, disease, and life expectancy.

2. Slide 6.4- 2 Copyright © 2009 Pearson Education, Inc. Risk and Travel Travel risk is often expressed in terms of an accident rate or death rate. For example, suppose an annual accident rate is 750 accidents per 100,000 people. This means that, within a group of 100,000 people, on average 750 will have an accident over the period of a year. The statement is in essence an expected value, which means it also represents a probability: It tells us that the probability of a person being involved in an accident (in one year) is 750 in 100,000, or 0.0075.

3. Slide 6.4- 3 Copyright © 2009 Pearson Education, Inc. Figure 6.11 shows the number of automobile fatalities and the total number of miles driven (among all Americans) for each year over a period of more than three decades. In terms of death rate per mile driven, how has the risk of driving changed? EXAMPLE 1 Is Driving Getting Safer? Figure 6.11 (a) Annual automobile fatalities. (b) Total miles driven annually. Both sets of data are for the United States only. Source: National Transportation Safety Board.

4. Slide 6.4- 4 Copyright © 2009 Pearson Education, Inc. Solution: Figure 6.11a shows that the annual number of fatalities decreased from about 52,000 in 1970 to about 43,000 in 2004. Meanwhile, Figure 6.11b shows that the number of miles driven increased from about 1,000 billion (1× 10 12 ) to about 2,900 billion (2.9 × 10 12 ). Therefore, the death rates per mile for the beginning and end of the period were 1970: ≈ 5.2 × 10 -8 death per mile 2004: ≈ 1.5 × 10 -8 death per mile 52,000 deaths 1 × 10 12 miles 43,000 deaths 2.9 × 10 12 miles

5. Slide 6.4- 5 Copyright © 2009 Pearson Education, Inc. Note that, because 10 8 = 100 million, 5.2 × 10 -8 death per mile is equivalent to 5.2 deaths per 100 million miles. Thus, over 34 years, the death rate per 100 million miles dropped from 5.2 to 1.5. By this measure, driving became much safer over the period. Most researchers believe the improvements resulted from better automobile design and from safety features, such as shoulder belts and air bags, that are much more common today. Solution: (cont.)

6. Slide 6.4- 6 Copyright © 2009 Pearson Education, Inc. Over the past 20 years in the United States, the average (mean) number of deaths in commercial airplane accidents has been roughly 100 per year. (The actual number varies significantly from year to year.) Currently, airplane passengers in the United States travel a total of about 8 billion miles per year. Use these numbers to calculate the death rate per mile of air travel. Compare the risk of flying to the risk of driving. EXAMPLE 2 Which Is Safer: Flying or Driving? Solution: Assuming 100 deaths and 8 billion miles in an average year, the risk of air travel is ≈ 1.3 × 10 -8 death per mile 100 deaths 8 × 10 9 miles

7. Slide 6.4- 7 Copyright © 2009 Pearson Education, Inc. Solution: (cont.) This risk is equivalent to 1.3 deaths per 100 million miles, or slightly lower than the risk of 1.5 deaths per 100 million miles for driving (see Example 1). Note that, because the average air trip covers a considerably longer distance than the average driving trip, the risk per trip is much higher for air travel, although the risk per mile is lower. EXAMPLE 2 Which Is Safer: Flying or Driving?

8. Slide 6.4- 8 Copyright © 2009 Pearson Education, Inc. TIME OUT TO THINK Suppose you need to make the 800-mile trip from Atlanta to Houston. Do you think it is safer to fly or to drive? Why?

9. Slide 6.4- 9 Copyright © 2009 Pearson Education, Inc. Vital Statistics Data concerning births and deaths of citizens, often called vital statistics, are very important to understanding risk-benefit tradeoffs. Demographers use birth and death rates to predict future population trends. One important set of vital statistics, shown in Table 6.8, concerns causes of death.

10. Slide 6.4- 10 Copyright © 2009 Pearson Education, Inc. EXAMPLE 3 Interpreting Vital Statistics Assuming a U.S. population of 300 million, find and compare risks per person and per 100,000 people for pneumonia (and influenza) and cancer. Solution: We find the risk per person by dividing the number of deaths by the total population of 300 million: Pneumonia /influenza: ≈ 0.00022 death per person Cancer: ≈ 0.0018 death per person 554,643 deaths 300,000,000 people 65,681 deaths 300,000,000 people

11. Slide 6.4- 11 Copyright © 2009 Pearson Education, Inc. EXAMPLE 3 Interpreting Vital Statistics We can interpret these numbers as probabilities: The probability of death by pneumonia or influenza is about 2.2 in 10,000, while the probability of death by cancer is about 18 in 10,000. To put them in terms of deaths per 100,000 people, we simply multiply the per person rates by 100,000. We get a pneumonia/influenza death rate of 22 deaths per 100,000 people and a cancer death rate of 180 deaths per 100,000 people. The probability of death by cancer is more than eight times that of death by pneumonia or influenza. Solution: (cont.)

12. Slide 6.4- 12 Copyright © 2009 Pearson Education, Inc. TIME OUT TO THINK Table 6.8 suggests that the probability of death by stroke is about 50% higher than the probability of death by accident, but these data include all age groups. How do you think the risks of stroke and accident would differ between young people and older people? Explain.

13. Slide 6.4- 13 Copyright © 2009 Pearson Education, Inc. Life Expectancy The idea of life expectancy is often used to compare overall health at different times or in different countries. Figure 6.12a The overall U.S. death rate (deaths per 1,000 people) for different ages. Figure 6.12a shows the overall U.S. death rate (or mortality rate), in deaths per 1,000 people, for different age groups.

14. Slide 6.4- 14 Copyright © 2009 Pearson Education, Inc. Figure 6.12b shows the life expectancy of Americans of different ages, defined as the number of years a person of a given age can expect to live on average. As we would expect, life expectancy is higher for younger people because, on average, they have longer left to live. At birth, the life expectancy of Americans today is about 78 years (75 years for men and 81 years for women). Figure 6.12b Life expectancy for different ages. Source: U.S. National Center for Health Statistics.

15. Slide 6.4- 15 Copyright © 2009 Pearson Education, Inc. Definition Life expectancy is the number of years a person with a given age today can expect to live on average.

16. Slide 6.4- 16 Copyright © 2009 Pearson Education, Inc. Figure 6.13 Changes in U.S. life expectancy during the 20th century. Source: New York Times and National Center for Health Science Statistics.

17. Slide 6.4- 17 Copyright © 2009 Pearson Education, Inc. TIME OUT TO THINK Using Figure 6.13 (previous slide), compare the life expectancies of men and women. Briefly discuss these differences. Do they have any implications for social policy? For insurance rates? Explain.

18. Slide 6.4- 18 Copyright © 2009 Pearson Education, Inc. EXAMPLE 4 Life Expectancies Using Figure 6.12b, find the life expectancy of a 20-year-old person and of a 60-year-old person. Are the numbers consistent? Explain. Solution: The graph shows that the life expectancy at age 20 is about 58 years and at age 60 is about 21 years. This means that an average 20-year-old can expect to live about 58 more years, to age 78. An average 60-year-old can expect to live about 21 more years, to age 81. Figure 6.12b

19. Slide 6.4- 19 Copyright © 2009 Pearson Education, Inc. Solution: (cont.) It might at first seem strange that 60-year-olds have a longer average life span than 20-year- olds (81 years versus 78 years). But remember that life expectancies are based on current data. If there were no changes in medicine or public EXAMPLE 4 Life Expectancies Figure 6.12b health, a 60-year-old would have a greater probability of reaching age 81 than a 20-year-old simply because he or she has already made it to age 60. However, if medicine and public health continue to improve, today’s 20-year-olds may live to older ages than today’s 60-year- olds.

20. TIME OUT TO THINK According to some biologists, there is a good chance that 21st-century advances in medical science will allow most people to live to ages of 100 or more. How would that affect programs like Social Security? What other effects would you expect it to have on society? Overall, do you think large increases in life expectancy would be good or bad for society? Defend your opinion. Copyright © 2009 Pearson Education, Inc. Slide 6.4- 20

21. Slide 6.4- 21 Copyright © 2009 Pearson Education, Inc. The End