We can see that 25-34 year olds have
the highest percentage of driver fatalities.
We can also see that 25-34 year olds also have the highest percentage
of
serious injuries.
We can see that the above dot plots
represent a bell shaped curve. The high
percentage value for 65+ is explained by the larger size of the
age group. Notice
also that the grouping for ages 15-24 is divided into 15-19 and
20-24. We should
also notice that the age groupings do not all have the same range.
I am allowing
this due to lack of normally distributed attributes concerning the
section of the
transportation industry with an understanding that this will affect
the probabilities
we will compute later. We will assume that these values represent
a population
that has a normal distribution.
To calculate the mean, µ , and
the standard deviation, ó , we use the formulas:
Note: We will isolate our data to ages 5-64 to avoid an overly high
mean due to
the jump of values at 65+. We will only be using m and s to create
a hypothetical
set of values to use for problem solving.
Driver Fatalities:
Driver with Serious Injuries:
Lets assume that the driver fatalities
are normally distributed with mean 30.5 with
standard deviation 13.3. Lets assume that the driver serious injuries
are normally
distributed with mean 31.2 with standard deviation 12.8. I will
now use Fathom to
create a sample of 250 values for age of fatalities and 250 values
for age of
serious injuries.
If the population is equal to 250
(let s ~= ó), what is the probability of a
driver who is killed is between 16 and 24 years old?
Therefore the probability a driver
who is killed is between 16 and 24 years
of age is 17.64%.
If we only have a sample of 250 people,
what is the probability of a driver that
is seriously injured is between 30 and 32?
Therefore the probability of a driver
that is seriously injured is between 30
and 32 is 22.1%.
What ages do 95% of driver fatalities occur?
Therefore 95% of driver fatalities occur between ages 17.7 and 43.3.
Consider the youngest 63% of drivers
with serious injuries. What is the oldest
driver with a serious injury?
We must find a corresponding z value to 0.63.
z=0.33
Therefore, concerning the youngest 63% of drivers with serious injuries,
the
oldest would be 35.424 years old.
Conclusion
I found that by using a modified x-axis (agegroup) I could use the
data (mean and
standard deviation) from the Motor Vehicle Statistics, whose graph
formed a bell
curve, to generate a hypothetical normal distribution to compare
ages with
serious injuries and fatalities in automobile accidents. We then
used the
properties of the normal distribution to solve problems relating
to probabilities
concerning age andinjuries including death.
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