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The Environmental Protection Agency (EPA) provides fuel economy estimates for automobile models tested recently, with a mean of 24.82 mpg and a standard deviation of 6.18 mpg for highway driving. Assuming a normal distribution, use the 68–95–99.7 rule to complete the following:

a) Draw the model for auto fuel economy, labeling it and showing what the 68–95–99.7 rule predicts.

Answer :

Using the 68-95-99.7 rule, we can draw the model for auto fuel economy given a mean and standard deviation.

The question asks to use the 68-95-99.7 rule to draw the model for auto fuel economy, given a mean of 24.82 mpg and a standard deviation of 6.18 mpg for highway driving.

  1. Step 1: Find the range within which 68% of the data falls by subtracting and adding one standard deviation from the mean. In this case, the range would be (24.82 - 6.18, 24.82 + 6.18) or (18.64, 31).
  2. Step 2: Repeat Step 1, but subtract and add two standard deviations from the mean to find the range within which 95% of the data falls. The range would be (24.82 - 2(6.18), 24.82 + 2(6.18)) or (12.46, 37.18).
  3. Step 3: Finally, subtract and add three standard deviations from the mean to find the range within which 99.7% of the data falls. The range would be (24.82 - 3(6.18), 24.82 + 3(6.18)) or (6.28, 43.36).

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