Question

(3.38) NOTE: The numerical values in this problem have been
modified for testing purposes. The quintiles of any distribution are the values with cumulative proportions 0.20, 0.40, 0.60, and 0.80. What are the quintiles of the distribution of gas mileage? (Use software) The first quintile is (±±0.01 mpg) mpg.______ The second quintile is (±±0.01 mpg) mpg._____ The third quintile is (±±0.01 mpg) mpg.____ The fourth quintile is (±±0.01 mpg) mpg._____ |

Answer #1

Suppose X follows approximately Normal with mean 22.9 miles per gallon (mpg) and standard deviation 5.2 mpg.

Here we need to find X scores for probabilities 0.20, 0.40, 0.60 and 0.80

Let's use excel:

For probability = 0.20

x = "=NORMINV(0.20, 22.9, 5.2)" = 18.52 mpg

**The first quintile is (±±0.01 mpg) mpg.
18.52**

For probability = 0.40

x = "=NORMINV(0.40, 22.9, 5.2)" = 21.58 mpg

**The second quintile is (±±0.01 mpg) mpg.
21.58**

For probability = 0.60

x = "=NORMINV(0.60, 22.9, 5.2)" = 24.22mpg

**The third quintile is (±±0.01 mpg) mpg.
24.22**

For probability = 0.80

x = "=NORMINV(0.80, 22.9, 5.2)" = 27.28 mpg

**The fourth quintile is (±±0.01 mpg) mpg.
27.28**

NOTE: The numerical values in this problem have been modified
for testing purposes.
In its Fuel Economy Guide for 2014 model vehicles, the
Environmental Protection Agency gives data on 1160 vehicles. There
are a number of high outliers, mainly hybrid gas-electric vehicles.
If we ignore the vehicles identified as outliers, however, the
combined city and highway gas mileage of the other 1134 vehicles is
approximately Normal with mean 23 miles per gallon (mpg) and
standard deviation 5.3 mpg.
The quintiles...

In its Fuel Economy Guide for 2014 model vehicles, the
Environmental Protection Agency gives data on 1160 vehicles. There
are a number of high outliers, mainly hybrid gas-electric vehicles.
If we ignore the vehicles identified as outliers, however, the
combined city and highway gas mileage of the other 1134 vehicles is
approximately Normal with mean 22.8 miles per gallon (mpg) and
standard deviation 5.3 mpg. The quintiles of any distribution are
the values with cumulative proportions 0.20, 0.40, 0.60, and...

In its Fuel Economy Guide for 2014 model vehicles, the
Environmental Protection Agency gives data on 1160 vehicles. There
are a number of high outliers, mainly hybrid gas-electric vehicles.
If we ignore the vehicles identified as outliers, however, the
combined city and highway gas mileage of the other 1134 vehicles is
approximately Normal with mean 22.8 miles per gallon (mpg) and
standard deviation 5.3 mpg.
The quintiles of any distribution are the values with cumulative
proportions 0.20, 0.40, 0.60, and...

In its Fuel Economy Guide for 2016 model vehicles, the
Environmental Protection Agency gives data on 1170 vehicles. There
are a number of high outliers, mainly hybrid gas-electric vehicles.
If we ignore the vehicles identified as outliers, however, the
combined city and highway gas mileage of the other 1146 vehicles is
approximately Normal with mean 23.0 miles per gallon and standard
deviation 4.9 mpg.
The quintiles of any distribution are the values with cumulative
proportions 0.20, 0.40, 0.60, and 0.80....

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