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Francis studied the population estimates of South Africa provided by Statistics SA for the years 2014 to 2016 - NSC Mathematical Literacy - Question 3 - 2017 - Paper 2

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Francis studied the population estimates of South Africa provided by Statistics SA for the years 2014 to 2016. TABLE 3 below shows population estimates, by group, f... show full transcript

Worked Solution & Example Answer:Francis studied the population estimates of South Africa provided by Statistics SA for the years 2014 to 2016 - NSC Mathematical Literacy - Question 3 - 2017 - Paper 2

Step 1

During 2015, the number of black females was estimated to be 41,1% of the total South African population. Determine the estimated total South African population (rounded off to the nearest 100) for 2015.

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Answer

To find the total South African population in 2015 based on the percentage of black females:

Let the total population be denoted as xx and the number of black females be 41.1% of xx.

According to the table, the number of black females in 2015 is 22,574,500. Thus, we can set up the equation:

0.411x=22,574,5000.411x = 22,574,500

Solving for xx gives:

x=22,574,5000.411≈54,925,800x = \frac{22,574,500}{0.411} \approx 54,925,800

Rounding to the nearest 100, the total estimated South African population in 2015 is approximately 54,925,800.

Step 2

If a person was randomly chosen in 2016, determine the probability that the person would be the following: (a) a white female

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Answer

To find the probability of selecting a white female in 2016:

According to the table, the number of white females in 2016 is 3,325,100.

The total South African population for 2016 is given as 95,908,000.

The probability PP of selecting a white female is:

P(white female)=Number of white femalesTotal population=3,325,10095,908,000≈0.0347P(\text{white female}) = \frac{\text{Number of white females}}{\text{Total population}} = \frac{3,325,100}{95,908,000} \approx 0.0347

Expressed as a percentage, this is approximately 3.47%.

Step 3

If a person was randomly chosen in 2016, determine the probability that the person would be the following: (b) a male

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Answer

To find the probability of selecting a male in 2016:

First, we need to find the total number of females based on the table, which gives:

Total females for 2016 = 35,200,000.

Then we can find the total males in 2016 as:

Total males=Total population−Total females=95,908,000−35,200,000=60,708,000.\text{Total males} = \text{Total population} - \text{Total females} = 95,908,000 - 35,200,000 = 60,708,000.

Now, the probability PP of selecting a male is:

P(male)=Number of malesTotal population=60,708,00095,908,000≈0.6326P(\text{male}) = \frac{\text{Number of males}}{\text{Total population}} = \frac{60,708,000}{95,908,000} \approx 0.6326

Expressed as a percentage, this is approximately 63.26%.

Step 4

Show, using calculations, that in any TWO consecutive years the Indian/Asian female percentage (rounded off to ONE decimal place) remained the same.

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Answer

To check if the Indian/Asian female percentage remained constant in consecutive years:

From the table:

  • For 2014: Indian/Asian females represent 1.0% of the population.
  • For 2015: Indian/Asian females also represent 1.0% of the population.
  • For 2016: Again, they represent 1.0%.

Thus, in all of the years 2014, 2015, and 2016, the percentage of Indian/Asian females remained consistently at 1.0%.

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