Mileage tests were conducted on a randomly selected sample of 100 newly developed automobile tires. The sample mean tread wear was 50,000 miles, with a population standard deviation of 3,500 miles. What is the best estimate of the average tread life in miles for the entire population of these tires?





The best estimate of the average tread life for the entire population of these tires is the **sample mean**, which is 50,000 miles. Since the sample mean is the unbiased estimator of the population mean, it is used as the best point estimate of the population's average tread life when you have a sample from a normally distributed population.

In this case:
- **Sample mean ( \(\bar{x}\) ) = 50,000 miles**
- **Population standard deviation ( \(\sigma\) ) = 3,500 miles**

So, the best estimate of the average tread life is:

\[
\boxed{50,000 \text{ miles}}
\]

Would you like more details on how confidence intervals can be used to refine this estimate?

Here are 5 related questions to deepen your understanding:
1. How would you calculate a 95% confidence interval for the population mean tread life based on this sample?
2. How does the sample size affect the precision of the population mean estimate?
3. What is the significance of knowing the population standard deviation versus just the sample standard deviation?
4. How would the estimate change if the sample size increased to 1,000 tires?
5. What assumptions must be satisfied to make the sample mean a reliable estimate of the population mean?

**Tip:** In cases where the population standard deviation is unknown, you can use the sample standard deviation and the t-distribution for more accurate estimates of the population mean.

Mileage tests were conducted on a randomly selected sample of 100 newly developed automobile tires. The sample mean tread wear was 50,000 miles, with a population standard deviation of 3,500 miles. What is the best estimate of the average tread life in miles for the entire population of these tires?

Find the best estimate of the average tread life for newly developed automobile tires using the sample mean. With a sample size of 100 and a standard deviation of 3,500 miles, the sample mean of 50,000 miles is used as the point estimate for the population mean. Ideal for Grades 10-12, this problem illustrates key statistical concepts like estimation and the population mean.

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