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A farm stall sells milk in 5-litre containers to the local community - NSC Mathematics - Question 2 - 2021 - Paper 2
Question 2
A farm stall sells milk in 5-litre containers to the local community. The price varies according to the availability of milk at the farm stall. The price of milk, in... show full transcript
Worked Solution & Example Answer:A farm stall sells milk in 5-litre containers to the local community - NSC Mathematics - Question 2 - 2021 - Paper 2
Step 1
2.1 On the grid provided in the ANSWER BOOK, draw the scatter plot to represent the data.
Answer
To create the scatter plot, you will need to plot the given data points where the x-axis represents the price of milk per 5-litre container, and the y-axis represents the number of containers sold. For each price, mark a point corresponding to the number of containers sold. Ensure to label your axes correctly and provide a title for the scatter plot.
Step 2
2.2 Determine the equation of the least squares regression line for the data.
Answer
To calculate the least squares regression line, we find coefficients a and b using the formulas:
a = rac{n( ext{sum}(xy)) - ( ext{sum}(x)( ext{sum}(y))}{n( ext{sum}(x^2)) - ( ext{sum}(x))^2}
b = rac{ ext{sum}(y) - a( ext{sum}(x))}{n}
Substituting the values yields the regression line equation:
y = ax + b, where a is the slope and b is the y-intercept.
Step 3
2.3 If the farmer sells a 5-litre container of milk for R38, predict the number of 5-litre containers of milk he will sell.
Answer
Using the equation obtained in Step 2.2, substitute x = 38 into the regression equation to calculate y.
This gives you a predicted value for the number of containers sold when the price is R38.
Step 4
2.4 Refer to the correlation between the price of 5-litre containers of milk and the number of 5-litre containers of milk sold, and comment on the accuracy of your answer to QUESTION 2.3.
Answer
The correlation coefficient (r = 0.94) indicates a strong positive relationship between the price of 5-litre containers and the number sold. This suggests that as the price increases, the number sold is likely to decrease. Given this strong correlation, the prediction made in 2.3 is expected to be fairly accurate.