Truck drivers travel a certain distance and have a rest before travelling further - NSC Mathematics - Question 1 - 2023 - Paper 2
Question 1
Truck drivers travel a certain distance and have a rest before travelling further. A driver kept record of the distance he travelled (in km) on 8 trips and the amoun... show full transcript
Worked Solution & Example Answer:Truck drivers travel a certain distance and have a rest before travelling further - NSC Mathematics - Question 1 - 2023 - Paper 2
Step 1
1.1 Determine the equation of the least squares regression line for the data.
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Answer
To find the least squares regression line, we compute the slope (b) and y-intercept (a) using the following formulas:
After calculating, we find the equation of the regression line as:
y=−23.85+0.23x
Step 2
1.2 If a truck driver travelled 550 km, predict the amount of time (in minutes) that he should rest before continuing his journey.
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Answer
To predict the rest time for a distance of 550 km, substitute x = 550 into the regression equation:
ar{y} = -23.85 + 0.23(550) = 102.65 ext{ minutes}
Step 3
1.3 Write down the correlation coefficient for the data.
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The correlation coefficient (r) for the data is 0.98, indicating a very strong positive correlation.
Step 4
1.4 Interpret your answer to QUESTION 1.3.
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Answer
The correlation coefficient of 0.98 suggests a very strong positive relationship between the distance travelled and the amount of rest time. This implies that as the distance increases, the amount of time spent resting also increases significantly.
Step 5
1.5.1 Calculate the mean amount of money he spent at each stop.
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Answer
To calculate the mean amount spent:
ar{x} = rac{ ext{Σ}x}{n} = rac{1200}{8} = 150 ext{ rands}
Step 6
1.5.2 Calculate the standard deviation for the data.
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The standard deviation (σ) can be calculated using the formula:
