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'n Padstal verkoop melk in 5 liter-houers aan die plaaslike gemeenskap - NSC Mathematics - Question 2 - 2021 - Paper 2
Question 2
'n Padstal verkoop melk in 5 liter-houers aan die plaaslike gemeenskap. Die prys wissel volgens die beskikbaarheid van melk by die padstal. Die prys van melk, in ran... show full transcript
Worked Solution & Example Answer:'n Padstal verkoop melk in 5 liter-houers aan die plaaslike gemeenskap - NSC Mathematics - Question 2 - 2021 - Paper 2
Step 1
2.1 Op die rooster wat in die ANTWOORDERBOEK verskaf word, teken die spreidiagram om die data te verteenwoordig.
Answer
To create a scatter plot for the given data, plot the price per 5-liter container (x-axis) against the number of containers sold (y-axis). Mark each data point accurately based on the corresponding values from the table. Label the axes appropriately with 'Price per 5-liter container (R)' on the x-axis and 'Number of 5-liter containers sold' on the y-axis.
Step 2
2.2 Bepaal die vergelyking van die kleinstekwadraat-regressielyn vir die data.
Answer
To find the least squares regression line, we use the formula for linearly fitting the data points. Utilizing the regression analysis, we calculate:
- The slope (b) of the regression line is approximately -1.77, and the intercept (a) is approximately 90.48. Thus, the equation of the regression line can be expressed as:
Step 3
2.3 Indien die prys von 5 liter-houer melk vir R38 verkoop, voorspel die aantal 5 liter-houers melk wat hy sal verkoop.
Answer
Using the regression equation determined in 2.2, substitute the price of R38 into the equation:
This computation will yield: Therefore, it is predicted that approximately 23 units of 5-liter containers will be sold.
Step 4
2.4 Verwys na die korrelasie tussen die prys van 5 liter-houers melk en die aantal 5 liter-houers melk verkoop, en gee kommentaar op die akkuraatheid van jou antwoord op VRAAG 2.3.
Answer
The correlation coefficient is calculated to be approximately -0.94, which indicates a strong negative relationship between the price of milk and the number of containers sold. This implies that as the price increases, the number of containers sold tends to decrease. Given this strong correlation, the prediction made in Question 2.3 is likely to be accurate.