Transcript Section 6.4 ~ Ideas of Risk and Life Expectancy

Section 6.4 ~
Ideas of Risk and Life Expectancy
Introduction to Probability and Statistics
Ms. Young
Sec. 6.4
Objective


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)
Sec. 6.4
Risk and Travel

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
Sec. 6.4
Example 1
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?
Sec. 6.4
Example 1 Cont’d…
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:
52, 000
8

4.3

10
 .000000043
12
1.2 10
• To put it into perspective, since
per 100 million miles
108 = 100 million, approximately 4.3 deaths occurred
• 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:
43, 000
8

1.5

10
 .000000015
12
2.9 10
• Again, since
miles
108 = 100 million, approximately 1.5 deaths occurred per 100 million
Sec. 6.4
Example 1 Cont’d…
Solution Cont’d:
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).
100 deaths
8

1.3

10
 .000000013 death per mile
9
8 10 miles
The risk is equivalent to 1.3 deaths per 100 million miles, which is slightly lower
than the average for driving.
Sec. 6.4
Vital Statistics

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
Sec. 6.4
Example 3
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.
65,681 deaths
Pneumonia/ influenza :
 0.00022 death per person
300,000,000 people
553,643 deaths
Cancer :
 0.0018 death per person
300,000,000 people
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.
Sec. 6.4
Life Expectancy

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

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
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 1000’s) by age

These types of graphs are often used to compare overall health at different
times or in different countries
Sec. 6.4
Life Expectancy Cont’d…

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)
Sec. 6.4
Example 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 life’s threats
whereas a 20 year old would have to live through 61 more years
which has a higher risk