This problem asks for the approximate percentage of cars that remain in service between 66 and 76 months using the 68-95-99.7 (Empirical) Rule. The rule tells us how data in a normal distribution is spread across standard deviations (σ) from the mean (μ).

Given:

• Mean (μ) = 61 months
• Standard deviation (σ) = 5 months
• We need to find the percentage of cars between 66 and 76 months.

1. 66 months is 1 standard deviation above the mean (66 - 61 = 5, which is 1σ).
2. 76 months is 3 standard deviations above the mean (76 - 61 = 15, which is 3σ).

Using the empirical rule:

• 68% of data falls within 1 standard deviation (from 56 to 66 months).
• 95% of data falls within 2 standard deviations (from 56 to 71 months).
• 99.7% of data falls within 3 standard deviations (from 56 to 76 months).

We are interested in the area between 66 and 76 months, which corresponds to the data between 1σ and 3σ. According to the rule:

• From 1σ to 2σ (66 to 71 months), about 13.5% of the data lies.
• From 2σ to 3σ (71 to 76 months), about 2.35% of the data lies.

So, the total percentage of cars between 66 and 76 months is: $13.5\% + 2.35\% = 15.85\%$

The approximate percentage is 15.85%.

Do you have any questions or want more details? Here are five related questions:

1. What does the 68-95-99.7 rule tell us about a normal distribution?
2. How would the result change if the standard deviation was larger?
3. What does "bell-shaped distribution" refer to in statistics?
4. How do you find probabilities for ranges not covered by the empirical rule?
5. How would you calculate the percentage for an interval not covered by full standard deviations?

Tip: The empirical rule is useful for quick approximations in normal distributions, but for more precision, you can use z-scores and a standard normal table.