To find the lowest mileage of the top 3% of the tires, we need to determine the 97th percentile (since the top 3% starts at this point) of a normal distribution with:

• Mean ($\mu$) = 47,500 miles
• Standard deviation ($\sigma$) = 3,000 miles

Excel Formula:

In Excel, use the NORM.INV function:

$\text{NORM.INV}(0.97, 47500, 3000)$

This function returns the mileage corresponding to the 97th percentile of the normal distribution.

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Step-by-step in Excel:

1. Open Excel.
2. In a cell, type the formula:

   =NORM.INV(0.97, 47500, 3000)
   

3. Press Enter to get the result.
4. Round the answer to the nearest integer.

Would you like me to explain this concept in more detail?

Here are 5 related questions for practice:

1. What mileage marks the lowest 5% of tires?
2. What percentage of tires last more than 50,000 miles?
3. What is the probability that a randomly selected tire lasts between 45,000 and 50,000 miles?
4. If a warranty covers tires lasting less than 43,000 miles, what percentage of tires will be covered?
5. How does increasing the standard deviation affect the distribution of tire lifespan?

Tip: In a normal distribution, the empirical rule (68-95-99.7) helps estimate probabilities without calculations! 🚀