Step 1 :The problem is asking for the probability that the sample mean tax is less than $8100. This is a problem of normal distribution.
Step 2 :The mean of the sample mean distribution is the same as the population mean, which is $8040.
Step 3 :The standard deviation of the sample mean distribution is the population standard deviation divided by the square root of the sample size, which is $4800 / \sqrt{1000}$.
Step 4 :We can then calculate the z-score for $8100, which is ($8100 - $8040) / ($4800 / \sqrt{1000}).
Step 5 :The probability that the sample mean tax is less than $8100 is the cumulative distribution function (CDF) of the normal distribution at this z-score.
Step 6 :Final Answer: The probability that the sample mean tax is less than $8100 is \(\boxed{0.6537}\).