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Timing Belt Life

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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