Question

Studies show that gasoline use for compact cars sold in the United States is normally distributed, with mean of 25.5 miles per gallon (mpg) and a standard deviation of 4.5 mpg. If a manufacturer wishes to develop a compact car that outperforms 95% of the current compacts in fuel economy, what must the gasoline use rate for the new car be?

Answer 1

Answer:

32.9 mpg

Step-by-step explanation:

Population mean (μ) = 25.5 mpg

Standard deviation (σ) = 4.5 mpg

Assuming a normal distribution for gasoline use, the manufacturer wants his car to be at the 95-th percentile of the distribution. The 95-th percentile has a corresponding z-score of 1.645. The expression for the z-score for a given gasoline use rate 'X' is:

$z=\frac{X-\mu}{\sigma} \\1.645=\frac{X-25.5}{4.5} \\X=32.9\ mpg$

The gasoline use rate for the new car must be at least 32.9 mpg