A major tire manufacturer wishes to estimate the mean tread life in miles for one of its tires. It wishes to develop a confidence interval estimate that would have a margin of error less than 400 miles with 99 percent confidence. Suppose the population standard deviation is equal to 4,000 miles. Based on this information, the required sample size should be at least:

1. 542
2. 543
3. 663
4. 664
5. None of the above