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.

1. What is the probability that the sample mean tax is less than $8000? Round the answer to at least four decimal places.
2. What is the probability that the sample mean tax is between $7400 and $8000? Round the answer to at least four decimal places.
3. Find the 60th percentile of the sample mean. Round the answer to at least one decimal place.
4. Would it be unusual if the sample mean were less than $7600? Round the answer to at least four decimal places.
5. Do you think it would be unusual for an individual to pay a tax of less than $7600? Explain. Assume the population is approximately normal. Round the answer to at least four decimal places.