Basic HTML Version
Q
uantitative
R
easoning &
P
roblem
S
olving
138
© 2014 Pacific Crest
M
ethodology
M
odeling a
R
andom
P
henomenon
with a
P
robability
D
istribution
Scenario:
A certain stretch of interstate requires commuters to change lanes and merge in a
short distance. After media reports that the area was not safe, the city decided to
study the safety of that portion of the interstate.
Step
Explanation
Watch it Work!
1.
What is the
random
phenomenon?
Identify the random phenomenon
and determine if it is possible to
model it
The number of car accidents per day
on a particular stretch of the interstate
is random and can be modeled
2.
Determine the
scope
In what contexts is the
phenomenon observed such that
data can be collected?
We would observe the same
phenomenon an any similar highway
layout
3.
Get reliable data
Use or produce an accurate data
set of the random phenomenon.
The size should be large enough
so that more data does not
change the observed behavior.
Accurate data was collected for the
entire year:
Accidents/Day Frequency
0
284
1
71
2
9
3
1
>3
0
4.
Construct a
Cumulative
Distribution
Use technology to construct a
table and graph of the cumulative
relative frequencies. To find
relative frequency, divide the
frequency by the sample size.
Accidents/Day Relative Frequency
0
284 / 365 ≈ 0.778
1
71 / 365 ≈ 0.195
2
9 / 365 ≈ 0.025
3
1 / 365 ≈ 0.003
>3
0 / 365 = 0
0
50
100
150
200
250
300
0
1
2
3
>3
accidents/day
frequency