The Internal Revenue Service reports that the mean federal income tax paid in a recent year was $8040. Assume that the standard deviation is $5000. The IRS plans to draw a sample of 1000 tax returns to study the effect of a new tax law.

a. What is the probability that the sample mean tax is less than $8000?

b. What is the probability that the sample mean tax is between $7600 and $7900?

c. Find the 40th percentile of the sample mean.

d. Would it be unusual if the sample mean were less than $7500?

e. Can you tell whether it would be unusual for an individual to pay a tax of less than $7500? Explain.