Transcript Section 6-4 Ideas of Risk

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.
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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.
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EXAMPLE 1 Is Driving Getting Safer?
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?
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.
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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× 1012) to
about 2,900 billion (2.9 × 1012).
Therefore, the death rates per mile for the beginning and end of
the period were
1970:
52,000 deaths
1 × 1012 miles
≈ 5.2 × 10-8 death per mile
2004:
43,000 deaths
2.9 × 1012 miles
≈ 1.5 × 10-8 death per mile
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Solution: (cont.)
Note that, because 108 = 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.
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EXAMPLE 2 Which Is Safer: Flying or Driving?
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.
Solution: Assuming 100 deaths and 8 billion miles in an
average year, the risk of air travel is
100 deaths
8 × 109 miles
≈ 1.3 × 10-8 death per mile
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EXAMPLE 2 Which Is Safer: Flying or Driving?
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.
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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?
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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.
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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:
65,681 deaths
300,000,000 people
≈ 0.00022 death per person
Cancer:
554,643 deaths
300,000,000 people
≈ 0.0018 death per person
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EXAMPLE 3 Interpreting Vital Statistics
Solution: (cont.)
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.
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Slide 6.4- 11
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.
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Slide 6.4- 12
Life Expectancy
The idea of life expectancy is often used to compare overall
health at different times or in different countries.
Figure 6.12a shows the
overall U.S. death rate (or
mortality rate), in deaths per
1,000 people, for different
age groups.
Figure 6.12a The overall U.S. death rate (deaths
per 1,000 people) for different ages.
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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.
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Definition
Life expectancy is the number of years a person with a
given age today can expect to live on average.
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Figure 6.13 Changes in U.S. life expectancy during the 20th century. Source:
New York Times and National Center for Health Science Statistics.
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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.
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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.
Figure 6.12b
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.
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EXAMPLE 4 Life Expectancies
Solution: (cont.)
It might at first seem strange that
60-year-olds have a longer
average life span than 20-yearolds (81 years versus 78 years).
But remember that life
expectancies are based on
current data. If there were no
Figure 6.12b
changes in medicine or public
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-yearolds.
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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.
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The End
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