A major U.S. automaker has determined that the city mileage for one of its new SUV models is normally distributed with a mean equal to 15.2 mpg. A report issued by the company indicated that 22 percent of the SUV model vehicles will get more than 17 mpg in the city. Given this information, what is the city mileage standard deviation for this SUV model?
A) 0.77 mpg
B) Approximately 2.34 mpg
C) 1.8 mpg
D) Approximately 3.1 mpg

Question

Quizplus · Accepted Answer

Given that 22% of the vehicles get more than 17 mpg, this corresponds to the upper tail of the normal distribution. The Z-score associated with the upper 22% of a normal distribution is approximately 0.78. Using the Z-score formula Z = (X - μ) / σ, where X is the value (17 mpg), μ is the mean (15.2 mpg), and σ is the standard deviation, we can solve for σ. Plugging in the values, 0.78 = (17 - 15.2) / σ, solving for σ gives approximately 2.31, which is closest to the provided option of approximately 2.34 mpg.

A Major US