Daily Fuel Expenditures in the Honda CRV versus Subaru Cross
Trek
Question: Daily city mileage for a taxi driver is
normally distributed with mean 120 miles and standard deviation 15 miles. Daily highway miles for a tax driver is
normally distributed with mean 50 miles and standard deviation 15 miles.
The EPA fuel efficiency estimates for the two cars are
presented below.
EPA fuel mileage for two
SUVs


City

Highway


Subaru XV Crosstrek

21

35

Honda CRV

16

32

The price of gasoline is uniformly distributed between $3.50
for $4.50
Use Excel simulation tools to estimate the average and the
standard deviation of fuel expenditures for this taxi driver if he uses a
Subaru CrossTrek and a Honda CRV.
Explain how the simulation is conducted.
Analysis: The Excel Function NORM.INV is used to
generate a vector of city and highway miles.
City miles = NORM.INV(RAND(),120,15)
Highway miles = NORM.INV(RAND(),50,15)
To get city
gallons divide city miles by city mpg.
To get highway
gallons divide highway miles by highway mpg.
Do this for the
Subaru and for the Honda.
Add city and
highway miles together to get total miles.
Generate a random
gas price with the rand() function
RGP (Random gas
price) = $1 x rand() + 3.50
Multiply RGP by
total gas consumed for the two cars.
Make many
observations by copying the first line.
Note Rand()
resets each time the spreadsheet is open so your actual numbers will differ
from mine. I hope that if large samples
are generated differences in summary statistic will be small.
First line of Simulated
Database


City Miles

130.7

Highway Miles

37.6

Subaru City Gallons

6.2

Subaru Highway Gallons

1.1

Total Subaru Gallons

7.3

Honda City Gallons

8.2

Honda Highway Gallons

1.2

Total Honda Gallons

9.3

Gas Price

$3.8

Gas Expenditure Subaru

$27.9

Gas Expenditure Honda

$35.8

Below are the
daily average and the daily standard deviation for the two SUVS given the daily
variation in amount driven (both city and highway) and the daily variation in
gasoline price.
Simulated Results For
Average Daily Gas Expenditure for
Subaru and Honda SUV Taxi
Cabs


Subaru
CrossTrek

Honda
CRV


Average

$28.8

$36.5

Standard Deviation

$4.1

$5.1

Concluding Remark: The purchase of the more fuelefficient
vehicle reduces average daily expenditures and the variability of expenditures
on gasoline. The results presented here are just one simulation based on one set of assumptions.
In some ways the vehicle miles traveled on highways assumption is unrealistic. Some people do not often travel on highways but when they do they travel large distances. STD=15 for highway vehicle miles traveled is very small but it would be wrong to just increase this number because it would result in many people having negative miles. Negative miles is not realistic, true.
See the appendix to this blog for a discussion of this issue.
An Appendix to the two SUV Simulation
http://dailymathproblem.blogspot.com/2014/08/thevehiclemilestraveledvariablein.htm
In some ways the vehicle miles traveled on highways assumption is unrealistic. Some people do not often travel on highways but when they do they travel large distances. STD=15 for highway vehicle miles traveled is very small but it would be wrong to just increase this number because it would result in many people having negative miles. Negative miles is not realistic, true.
See the appendix to this blog for a discussion of this issue.
An Appendix to the two SUV Simulation
http://dailymathproblem.blogspot.com/2014/08/thevehiclemilestraveledvariablein.htm
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