Question

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 $490. 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 $8200? Round the answer to at least four decimal places.
The probability that the sample mean tax is less than $8200 is?

Part 2 of 5
(b) What is the probability that the sample mean tax is between $7500 and $8100? Round the answer to at least four decimal places.

The probability that the sample mean tax is between $7500 and $8100 is?

Part 3 of 5
(c) Find the 60th percentile of the sample mean. Round the answer to at least two decimal places.
The 60th percentile of the sample mean is?

Part 4 of 5
(d) Would it be unusual if the sample mean were less than $7800? Round answer to at least four decimal places.
It (is/isnt) unusual because the probability of the sample mean being less than $7800 is?

Part 5 of 5
(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/no), because the probability that an individual to pays a tax less than $7800 is?

Answer 1

a) P( < 8200)

= P(Z < 10.33)

= 1

b) P(7500 < < 8100)

= P(-34.85 < Z < 3.87)

= P(Z < 3.87) - P(Z < -34.85)

= 1 - 0 = 1

c) P( < x) = 0.60

d) P( < 7800)

= P(Z < -15.49)

= 0

e) Yes, because the probability that an individual to pays a tax less than $7800 is less than 0.05. So it is unusual.