Section 6.4 ~ Ideas of Risk and Life Expectancy Introduction to Probability and Statistics Ms. Young

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)

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 Sec. 6.4

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?

Example 1 Cont’d… 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 miles

Example 1 Cont’d… Sec. 6.4 Solution Cont’d: From 1970 to 2004 the death rates decreased about 65% (( )/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.

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 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 ( x 100,000) for pneumonia/influenza and 180 deaths per 100,000 people (.0018 x 100,000) for cancer.

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 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 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 life’s threats whereas a 20 year old would have to live through 61 more years which has a higher risk