A cricket is an insect - HSC - SSCE Mathematics Standard - Question 36 - 2020 - Paper 1
Question 36
A cricket is an insect. The male cricket produces a chirping sound.
A scientist wants to explore the relationship between the temperature in degrees Celsius and t... show full transcript
Worked Solution & Example Answer:A cricket is an insect - HSC - SSCE Mathematics Standard - Question 36 - 2020 - Paper 1
Step 1
Find the value of \(\bar{x}\)
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Answer
Given that the mean temperature is 0.525°C below the median, let the median be (\bar{x} = 22°C). Thus, we find:
[\bar{x} = 22 - 0.525 = 21.475°C]
Step 2
Find the value of \(\bar{y}\)
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Answer
The total number of chirps counted is 684. Since data is collected over 20 days, we calculate the mean:
[\bar{y} = \frac{684}{20} = 34.2]
Step 3
Substituting \(\bar{x}\) and \(\bar{y}\) into the regression equation
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Now we substitute the values we found into the regression equation:
[34.2 = -10.6063 + b \cdot 21.475]
[34.2 + 10.6063 = b \cdot 21.475]
[44.8063 = b \cdot 21.475]
[b = \frac{44.8063}{21.475} \approx 2.08644]
Step 4
Calculate the expected number of chirps when temperature is 19° Celsius
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Answer
Now we can find the expected number of chirps when (x = 19):
