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 $4600. 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$8100? Round the answer to at least four decimal places.

(b) What is the probability that the sample mean tax is between $7500 and $8100? Round the answer to at least four decimal places. (c) Find the 70th percentile of the sample mean. Round the answer to at least two decimal places.

(d) Would it be unusual if the sample mean were less than $7800? Round answer to at least four decimal places.

It (is or is not) unusual because the probability of the sample mean being less than $7800is?

(e) Do you think it would be unusual for an individual to pay a tax of less than$7800? Explain. Assume the variable is normally distributed. Round the answer to at least four decimal places.

(Yes or No) because the probability that an individual to pays a tax less than$7800 is?