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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.

A company has a policy of retiring company cars; this policy looks at the number of miles driven, purpose of trips, style of car, and other features. The distribution of the number of months in service for the fleet of cars is bell-shaped and has a mean of 61 months and a standard deviation of 5 months. Using the 68-95-99.7 (Empirical) Rule, what is the approximate percentage of cars that remain in service between 66 and 76 months?

Learn how to calculate the percentage of cars remaining in service between 66 and 76 months using the Empirical Rule. With a mean of 61 months and a standard deviation of 5 months, this problem demonstrates key statistical concepts related to normal distributions.

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