Question

Fuel economy estimates for automobiles built one year predicted a mean of 26.8 mpg and a standard deviation of 7.02 mpg for highway driving. Assuming the gas mileages for automobiles are normally distributed, use the Empirical Rule to answer the following:

• The middle 99.7% of automobiles can be expected to have gas mileages between____ and_____ .
• Approximately______ % of automobiles will have a gas mileage more than 19.78 mpg.
• Approximately______ % of automobiles will have gas mileages between 19.78 and 40.84.
• Which of the statements below describes the gas mileages of the best 2.5% of cars?
  • They get more than 40.84 mpg.
  • They get less than 12.76 mpg.
  • They get less than 5.74 mpg.
  • They get more than 47.86 mpg.

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Answer 1

26.8 - 3*7.02 = 5.74
26.8 + 3*7.02 = 47.86

The middle 99.7% of automobiles can be expected to have gas mileages between 5.74 and 47.86.

(1 - 0.16) = 0.84
Approximately 84 % of automobiles will have a gas mileage more than 19.78 mpg.

0.84 - 0.025 = 0.815
Approximately 81.5% of automobiles will have gas mileages between 19.78 and 40.84.

They get more than 40.84 mpg.