Answered: Taxes: The Internal Revenue Service…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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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

$4900

. 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

$7800

? Round the answer to at least four decimal places.

The probability that the sample mean tax is less than

$7800

0.3121

Part 2 of 5

(b) What is the probability that the sample mean tax is between

$7500

and

$8000

? Round the answer to at least four decimal places.

The probability that the sample mean tax is between

$7500

and

$8000

Part 3 of 5

30th

percentile of the sample mean. Round the answer to at least two decimal places.

The

30th

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 ▼(Choose one) unusual because the probability of the sample mean being less than

$7800

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.

▼(Choose one), because the probability that an individual to pays a tax less than

$7800

Taxes: The Internal Revenue Service reports chac che mean federal income tax bald in the year 2010was $8040 Assume choc che standard deviation is $4900 The
JRS plans to draw a sample of 1000cax returns to study the effect of a new cax law.
Part 1 of 5
(a) What is the probability chache sample mean cox is less than $7800 Round the answer to at least four decimal places.
The orosolicy chac che sample mean cax is less than $7800 03121
Part 2 of 5
x
10) What is the propolicy chache sample mean cax is between $7500 and $8000 Round one answer to at least four decimal places.
The orosolicy chac che sample mean cax is between $7500 and $8000
Part 3 of 5
Ic) Find one 30 percentile of the sample mean. Round the answer to at least two decimal places.
The 30 percentile of the sample means $
x
Part 4 of 5
(d) Would it be unusual che sample mean were less than $7800 Round answer to at least four decimal places.
Jc Choose one)
unusual because the propolicy of the sample mean being less than $7800

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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