Section 6.4 ~ Ideas of Risk and Life Expectancy

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Section 6.4 Ideas of Risk and Life Expectancy

• Introduction to Probability and Statistics
• Ms. Young

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Objective
Sec. 6.4

• After this section you will be able to compute
  and interpret various measures of risk as they
  apply to travel, disease, and life expectancy.
• The cost of living is going up and the chance of
  living is going down.
• - Flip Wilson (Comedian)

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Risk and Travel
Sec. 6.4

• Travel risk is often expressed in terms of an
  accident rate or death rate and is scaled to a
  certain unit (miles, years, people, etc.)
• Ex. 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
Sec. 6.4
The graphs below show the number of automobile
fatalities (on left) and the total number of
miles driven among all Americans (on right) for
each year over a period of more than three
decades. In terms of the death rate per mile
driven, how has the risk of driving changed?
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Example 1 Contd
Sec. 6.4

• In order to figure out the death rate per mile
  driven, you must compare the total number of
  deaths to the total number of miles driven
• In 1970, there were approximately 52,000
  deaths and approximately a total of
• 1200 billion (1.2 trillion or
  1,200,000,000,000) miles were driven, so the
  death
• rate per mile in 1970 was
• To put it into perspective, since 100
  million, approximately 4.3 deaths occurred
• per 100 million miles
• In 2004, there were approximately 43,000
  deaths and approximately a total of
• 2900 billion (2.9 trillion or
  2,900,000,000,000) miles were driven, so the
  death
• rate per mile in 2000 was
• Again, since 100 million, approximately
  1.5 deaths occurred per 100 million

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Example 1 Contd
Sec. 6.4

• Solution Contd
• From 1970 to 2004 the death rates decreased
  about 65 ((4.3-1.5)/4.3) which
• tells us that driving has become much safer
  over this period of time. This
• mostly likely is a result of better safety
  design with automobiles today such as
• shoulder belts and air bags.

Example 2
Over the past 20 years in the United States, the
average number of deaths in commercial airplane
accidents has been roughly 100 per 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 (found in
example 1). The risk is equivalent to 1.3
deaths per 100 million miles, which is slightly
lower than the average for driving.
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Vital Statistics
Sec. 6.4

• Data concerning births or deaths of citizens are
  often called vital statistics
• Uses of vital statistics in the real world
• Insurance companies use vital statistics to
  assess risks and set rates
• Health professionals study vital statistics to
  assess medical progress and decide where research
  resources need to be concentrated
• Demographers use birth and death rates to predict
  future population trends

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Example 3
Sec. 6.4
The table on page 262 represents the number of
deaths recorded in a year study of the leading
causes of death. Assuming the U.S. population is
300 million, find and compare the risks per
person and per 100,000 people for pneumonia (and
influenza) and cancer.
These death rates equate to 22 deaths per 100,000
people (.00022 x 100,000) for pneumonia/influenza
and 180 deaths per 100,000 people (.0018 x
100,000) for cancer.
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Life Expectancy
Sec. 6.4

• Life expectancy is the number of years a person
  of a given age can expect to live on average
• It is calculated by studying current death rates
• Life expectancies have increased dramatically
  during the past century because of advances in
  both medical science and public health
• If this trend continues, infants today are likely
  to live much longer than infants years ago
• The following graph shows the U.S. death rate (in
  1000s) by age
• These types of graphs are often used to compare
  overall health at different times or in different
  countries

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Life Expectancy Contd
Sec. 6.4

• The following graph shows the U.S. life
  expectancy by age
• As expected, life expectancy is higher for
  younger people because they have longer left to
  live on average
• The life expectancy at birth currently is 78
  years on average (75 years for men and 81 years
  for women)

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Example 4
Sec. 6.4
Who has a greater probability of living until
they are 81 years old? A 20 year old who has
roughly 61 years to live or a 60 year old who has
roughly 21 years to live. Using common sense, a
60 year old has better chances of living until 81
since they have already lived through most of
lifes threats whereas a 20 year old would have
to live through 61 more years which has a higher
risk