Questions: In fuel economy tests in city driving conditions, a hybrid vehicle's mean was 45.0 mpg with a standard deviation of 2.2 mpg . A comparably sized gasoline vehicle's mean was 34.0 mpg with a standard deviation of 3.2 mpg . Which vehicle's mpg was more consistent in relative terms? (Round your answers to 1 decimal places.)

Solution Steps

To determine which vehicle's mpg was more consistent in relative terms, we can calculate the coefficient of variation (CV) for each vehicle. The CV is the ratio of the standard deviation to the mean, expressed as a percentage. A lower CV indicates more consistency.

1. Calculate the CV for the hybrid vehicle: \( \text{CV}_{\text{hybrid}} = \left(\frac{\text{standard deviation}}{\text{mean}}\right) \times 100 \).
2. Calculate the CV for the gasoline vehicle: \( \text{CV}_{\text{gasoline}} = \left(\frac{\text{standard deviation}}{\text{mean}}\right) \times 100 \).
3. Compare the CVs to determine which vehicle's mpg is more consistent.

The coefficient of variation (CV) is calculated using the formula:

\[ \text{CV}_{\text{hybrid}} = \left(\frac{\text{standard deviation}}{\text{mean}}\right) \times 100 \]

Substituting the given values for the hybrid vehicle:

\[ \text{CV}_{\text{hybrid}} = \left(\frac{2.2}{45.0}\right) \times 100 = 4.8889 \]

Rounding to four significant digits, we have:

\[ \text{CV}_{\text{hybrid}} = 4.889 \]

Similarly, calculate the CV for the gasoline vehicle:

\[ \text{CV}_{\text{gasoline}} = \left(\frac{\text{standard deviation}}{\text{mean}}\right) \times 100 \]

Substituting the given values for the gasoline vehicle:

\[ \text{CV}_{\text{gasoline}} = \left(\frac{3.2}{34.0}\right) \times 100 = 9.4118 \]

Rounding to four significant digits, we have:

\[ \text{CV}_{\text{gasoline}} = 9.412 \]

To determine which vehicle's mpg is more consistent, compare the CVs:

• \(\text{CV}_{\text{hybrid}} = 4.889\)
• \(\text{CV}_{\text{gasoline}} = 9.412\)

Since \(4.889 < 9.412\), the hybrid vehicle's mpg is more consistent.

Final Answer