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To solve this, let's break down the information given:

1. **Mean tire life** (\(\mu\)) = 30,000 km
2. **Standard deviation** (\(\sigma\)) = 2,000 km
3. The question specifies that **68%** of the tire life values will fall within a certain range.

In a normal distribution, 68% of data falls within **one standard deviation** from the mean. This range can be calculated as:

\[
\text{Lower limit} = \mu - \sigma = 30,000 - 2,000 = 28,000 \, \text{km}
\]
\[
\text{Upper limit} = \mu + \sigma = 30,000 + 2,000 = 32,000 \, \text{km}
\]

Therefore, 68% of all tires will have a life between **28,000 km and 32,000 km**.

The correct answer is:
**28,000 km and 32,000 km**.

Would you like more details or have any questions?

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Here are 5 related questions to expand your understanding:

1. What percentage of values fall within two standard deviations from the mean in a normal distribution?
2. How would the range change if we were looking for 95% of all tires?
3. What is the probability of a tire lasting less than 28,000 km?
4. How can we calculate the probability of a tire lasting more than 32,000 km?
5. What would the range be for 99.7% of the tire life values?

**Tip:** In a normal distribution, approximately 68% of data falls within 1 standard deviation, 95% within 2, and 99.7% within 3.

The mean life of a tire is 30,000 km. The standard deviation is 2000 km. Then, 68% of all tires will have a life between _________ km and _________ km.

Learn how to calculate the tire life range with a mean of 30,000 km and a standard deviation of 2000 km. Using the Empirical Rule, find the range where 68% of tires will fall, ideal for high school statistics.

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