Step 1 :Given that the sample mean BAC is 0.15 g/dL, the standard deviation is 0.08 g/dL, and the sample size is 51 drivers.
Step 2 :We are asked to determine a 90% confidence interval for the mean BAC in fatal crashes in which the driver had a positive BAC.
Step 3 :The formula for a confidence interval is given by \( \text{sample mean} \pm z \times \left(\frac{\text{standard deviation}}{\sqrt{\text{sample size}}}\right) \).
Step 4 :The z-value for a 90% confidence interval is 1.645.
Step 5 :Substituting the given values into the formula, we get \( 0.15 \pm 1.645 \times \left(\frac{0.08}{\sqrt{51}}\right) \).
Step 6 :Solving the above expression, we get the confidence interval as \( (0.1315723140941914, 0.1684276859058086) \).
Step 7 :Rounding to three decimal places, we get the confidence interval as \( (0.132, 0.169) \).
Step 8 :\(\boxed{\text{Final Answer: The researcher is 90% confident that the population mean BAC is between 0.132 and 0.169 for drivers involved in fatal accidents who have a positive BAC value.}}\)