Mileage tests were conducted on a randomly selected sample of 100 newly developed automobile tires. The average tread wear was found to be 50,000 miles with a 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?
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A. B. C. D. E.Explanation
The sample mean is a good estimate of the population mean.
To estimate the average tread life in miles for the entire population of these tires, we can use the concept of sampling distribution and the Central Limit Theorem.
The Central Limit Theorem states that if we have a large enough sample size, regardless of the shape of the population distribution, the sampling distribution of the sample mean will be approximately normally distributed. The mean of the sampling distribution will be equal to the population mean, and the standard deviation of the sampling distribution (also known as the standard error) can be estimated using the formula:
Standard Error = Standard Deviation / √(Sample Size)
In this case, the sample size is 100, and the standard deviation of the tread wear is 3,500 miles.
So, the standard error = 3,500 / √(100) = 3,500 / 10 = 350 miles.
Now, since the average tread wear of the sample is 50,000 miles, we can use this as the best estimate of the population mean, as long as the conditions for the Central Limit Theorem are met (i.e., random sampling and a sufficiently large sample size). Therefore, the correct answer is D. 50,000 miles.