Question

a motorcycles fuel efficiency represents the ninth decile of vehicles in its class. make an observation about the motorcycles fuel efficiency.

choose the correct answer below.

a. the motorcycles fuel efficiency is greater than the fuel efficiency for 90% of vehicles in its class.
b. the motorcycles fuel efficiency is greater than the fuel efficiency for 9% of vehicles in its class.
c. the motorcycles fuel efficiency is greater than the fuel efficiency for 10% of vehicles in its class.
d. the motorcycles fuel efficiency is greater than the fuel efficiency for 100% of vehicles in its class.

Explanation:

Define the concept of deciles

Using the Percentiles and Quantiles knowledge point

$$ D_k = P_{10k} $$

Deciles divide an ordered dataset into ten equal parts, where the \(k\)-th decile \(D_k\) corresponds directly to the \(10k\)-th percentile.

Interpret the ninth decile

Using the Percentiles and Quantiles knowledge point

$$ D_9 = P_{90} $$

The ninth decile (\(D_9\)) is equivalent to the 90th percentile (\(P_{90}\)), meaning that approximately \(90\%\) of the observations fall below this value.

Evaluate the given options

Using the Percentiles and Quantiles knowledge point

• Option A states the fuel efficiency is greater than \(90\%\) of vehicles, which matches \(P_{90}\).
• Option B states it is greater than \(9\%\) of vehicles.
• Option C states it is greater than \(10\%\) of vehicles.
• Option D states it is greater than \(100\%\) of vehicles.

Therefore, Option A is the correct interpretation.

Answer:

• A. The motorcycle's fuel efficiency is greater than the fuel efficiency for 90% of vehicles in its class. (Correct answer)
• B. The motorcycle's fuel efficiency is greater than the fuel efficiency for 9% of vehicles in its class.
• C. The motorcycle's fuel efficiency is greater than the fuel efficiency for 10% of vehicles in its class.
• D. The motorcycle's fuel efficiency is greater than the fuel efficiency for 100% of vehicles in its class.