The Internal Revenue Service (IRS) reports that the mean federal income tax paid in a recent year was $8270. Assume that the standard deviation is $6000. A sample of 87 IRS tax filers for that year is randomly selected. Round answers to FOUR decimal places.

a) What is the probability that the mean federal income tax paid for the sample is less than $7900?

b) What is the probability that the mean federal income tax paid for the sample is more than $9500?

c) What is the probability that the mean federal income tax paid for the sample is between $8000 and $8450?