Step 1 :Given that the sample mean (\(\bar{x}\)) is 0.17, the standard deviation (s) is 0.06, and the sample size (n) is 82. The z-score for a 90% confidence interval is approximately 1.645.
Step 2 :We can calculate the margin of error using the formula \(z \frac{s}{\sqrt{n}}\). Substituting the given values, we get a margin of error of approximately 0.0109.
Step 3 :We can then calculate the lower and upper bounds of the confidence interval by subtracting and adding the margin of error from the sample mean respectively. This gives us a lower bound of approximately 0.159 and an upper bound of approximately 0.181.
Step 4 :\(\boxed{\text{Final Answer: The researcher is 90% confident that the population mean BAC is between 0.159 and 0.181 for drivers involved in fatal accidents who have a positive BAC value.}}\)