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.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.

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Asked Nov 4, 2019

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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.

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.

Expert Answer

Step 1

Given from question,

Mean (μ) =$8040, standard deviation (σ) =$4900 and sample size (n) =1000.

Step 2

Standard deviation for the sample mean is

Image Transcription
4900 V1000 154.9516053483=154.95

Step 3

If an individual to pay a tax of less than $7800 is in between the mean to 2sigma point (2σ) is called as a usual value or usual amount othe...

Image Transcription
H-20-8040-(2x154.95) =$7730.1000 H+20040+(2x154.95) $8349.9000

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