Answered: The Internal Revenue Service reports…

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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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 $4700. 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? Round the answer to at least four decimal places. The probability that the sample mean tax is less than $8000 is___ (b) What is the probability that the sample mean tax is between $7600 and $8100? Round the answer to at least four decimal places The probability that the sample mean tax is between $7600 and $8100 is_______ (c) Find the 30th percentile of the sample mean. Round the answer to at least two decimal places. The 30th percentile of the sample mean is_____ (d) Would it be unusual if the sample mean were less than $7600? Round answer to at least four decimal places. It would/would not be unusual because the probability of the sample mean being less than $7600 is___ (e) Do you think it would be unusual for an individual to pay a tax of less than $7600? 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 $7600 is____

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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