(Solved): Taxes: The Internal Revenue Service reports that the mean federal income tax paid in the year2010was ...

Taxes: The Internal Revenue Service reports that the mean federal income tax paid in the year 2010 was $\$8040$. Assume that the standard deviation is $\$4500$. The IRS plans to draw a sample of 1000 tax returns to study the effect of a new tax law. Part 1 of 5 (a) What is the probability that the sample mean tax is less than $\$7800$ ? Round the answer to at least four decimal places. The probability that the sample mean tax is less than $\$7800$ is Part 2 of 5 (b) What is the probability that the sample mean tax is between $\$7400$ and $\$7900$ ? Round the answer to at least four decimal places. The probability that the sample mean tax is between $\$7400$ and $\$7900$ is Part 3 of 5 (c) Find the $10^{\text{th }}$ percentile of the sample mean. Round the answer to at least one decimal place. The $10^{\text{th }}$ percentile of the sample mean is $\$$