Q.2.102 - Elementary Statistics

Question

Adjusted Gross Incomes. The Internal Revenue Service (IRS) publishes data on adjusted gross incomes in Statistics of Income, and Individual Income Tax Returns. The following relative frequency histogram shows one year's individual income tax returns for adjusted gross incomes of less than $\backslash (50,000$.

Use the histogram and the fact that adjusted gross incomes are expressed to the nearest whole dollar to answer each of the following questions.

a. Approximately what percentage of the individual income tax returns had an adjusted gross income between$\backslash )10,000$ and $\backslash (19,999$, inclusive?

b. Approximately what percentage had an adjusted gross income of less than $\backslash )30,000$ ?

c. The IRS reported that $\backslash (89,928,000$ individual income tax returns had an adjusted gross income of less than $\backslash )50,000$. Approximately how many had an adjusted gross income between $\backslash (30,000$ and $\backslash )49,999$, inclusive?

Step-by-Step Solution

Answer

a). The percent of individual income tax return had an adjusted gross income between $\$10,000$and $\$19,999$ is $\$0.28$ or $28\%$ because the height of second bar is about $\$0.28$.

b). The percent of individual income tax return had an adjusted gross income less than $\$30,000$, is $85\%$.

c). The percent of individual income tax return had an adjusted gross income between $\$30,000$ and $\$49,999$ is,$13,489,200$.

Part (a) Step 1: Given Information

The data is given as,

Part (a) Step 2: Explanation

Gross income minus income adjustments equals adjusted gross income (AGI). Wages, dividends, capital gains, company revenue, retirement distributions, and other sources of income are all included in gross income.

According to the given information, the height of the second bar is nearest to $0.28$

Part (b) Step 1: Given Information

The data is given as,

Part (b) Step 2: Explanation

The percent of individual income tax return had an adjusted gross income less than $\$30,000$will be:

$0.38+0.28+0.19=0.85\text{ or }85\%$.

Part (c) Step 1: Given Information

The data is given as,

Part (c) Step 2: Explanation

The percent of individual income tax return had an adjusted gross income between $\$30,000$ and $\$49,999$ is,

$0.15(89,928,000)=13,489,200$.