Use the above data to answer the questions that follow. 3.1.1 Calculate missing value C. 3.1.2 Determine, to THREE decimal places, the probability of randomly choosing an assessed taxpayer if South Africa's population was 57,73 million in 2018. 3.1.3 Calculate, in rand, the mean monthly taxable income per taxpayer in the R70 001 to R350 000 taxable income group. 3.1.4 In the table, the percentage for tax assessed is 0,0% for the taxable income group R1 to R70 000. Explain, showing calculations, how this percentage was obtained.

NSC Mathematical Literacy The probability scale: Use the above data to answer the

Use the above data to answer the questions that follow - NSC Mathematical Literacy - Question 3 - 2021 - Paper 2

Question 3

Use the above data to answer the questions that follow. 3.1.1 Calculate missing value C. 3.1.2 Determine, to THREE decimal places, the probability of randomly choo... show full transcript

Worked Solution & Example Answer:Use the above data to answer the questions that follow - NSC Mathematical Literacy - Question 3 - 2021 - Paper 2

Step 1

Calculate missing value C.

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Answer

To find the missing value C, we first calculate the total taxable income. The sum of the amounts assessed from all the income groups is:

$C = -16 302 + 15 030 + 577 196 + 297 012 + 783 526$

Calculating this gives:

$C = 1 656 462$

Thus, the missing value for C is R1 656 462 million.

Step 2

Determine, to THREE decimal places, the probability of randomly choosing an assessed taxpayer.

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Answer

The probability of randomly selecting an assessed taxpayer can be found using the formula:

$P = \frac{n}{N}$

where:

n = number of assessed taxpayers = 4 917 029
N = total population of South Africa = 57.73 million = 57 730 000.

Thus, we compute:

$P = \frac{4 917 029}{57 730 000} \approx 0.085$

Rounded to three decimal places, this gives a probability of 0.085.

Step 3

Calculate, in rand, the mean monthly taxable income per taxpayer in the R70 001 to R350 000 taxable income group.

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Answer

To find the mean monthly taxable income in this group, we first find the total taxable income for that group:

$\frac{577 196 \text{ million}}{2 856 043} = 202 096.297$

Converting this to the monthly mean:

$\frac{R202 096.297}{12} \approx R16 841.3573$

Thus, the mean monthly taxable income per taxpayer in this group is approximately R16 841.36.

Step 4

Explain how the percentage for tax assessed of 0,0% for taxable income group R1 to R70 000 was obtained.

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Answer

The tax assessed for the taxable income group R1 to R70 000 is given as:

Tax assessed: -R16 302 million
Total assessed tax: R356 199 million.

To find the percentage:

$\text{Percentage} = \frac{-16 302}{356 199} \times 100\% \approx -0.0458\% \approx 0.0\%\text{ (rounded)}$

Thus, the percentage is reported as 0.0%.

Use the above data to answer the questions that follow - NSC Mathematical Literacy - Question 3 - 2021 - Paper 2

Worked Solution & Example Answer:Use the above data to answer the questions that follow - NSC Mathematical Literacy - Question 3 - 2021 - Paper 2

Calculate missing value C.

Determine, to THREE decimal places, the probability of randomly choosing an assessed taxpayer.

Calculate, in rand, the mean monthly taxable income per taxpayer in the R70 001 to R350 000 taxable income group.

Explain how the percentage for tax assessed of 0,0% for taxable income group R1 to R70 000 was obtained.

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