Timing Belt Life
1. **State the problem:** We have timing belt lifespans with some censored data (8+ means the belt lasted at least 8 years but exact failure time is unknown).
2. **Data given:** Lifespans are 6.2, 5, 6.6, 8+, 8+ years.
3. **Median calculation:** Arrange known and censored data in ascending order: 5, 6.2, 6.6, 8+, 8+.
Since 8+ means at least 8, the median is the middle value of the ordered data.
The middle (3rd) value is 6.6 years.
So, the median timing belt life is **6.6 years**.
4. **Mean calculation:** The mean is the average lifespan.
For censored data, the exact failure time is unknown but at least 8 years.
So, the mean is at least the average of (6.2, 5, 6.6, 8, 8) where we use 8 as a minimum for censored values.
Calculate mean lower bound:
$$\frac{6.2 + 5 + 6.6 + 8 + 8}{5} = \frac{33.8}{5} = 6.76$$
Thus, the mean timing belt life is **greater than 6.76 years**.
**Final answers:**
- Median timing belt life = $6.6$ years
- Mean timing belt life > $6.76$ years