Dian uses the large data set to investigate the Daily Total Rainfall, r mm, for Camborne - Edexcel - A-Level Maths Statistics - Question 3 - 2022 - Paper 1
Question 3
Dian uses the large data set to investigate the Daily Total Rainfall, r mm, for Camborne.
(a) Write down how a value of 0 < r ≤ 0.05 is recorded in the large data s... show full transcript
Worked Solution & Example Answer:Dian uses the large data set to investigate the Daily Total Rainfall, r mm, for Camborne - Edexcel - A-Level Maths Statistics - Question 3 - 2022 - Paper 1
Step 1
How a value of 0 < r ≤ 0.05 is recorded in the large data set.
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Answer
In the large data set, values of rainfall that fall within the range of 0 to 0.05 mm are typically recorded as 0.00 to indicate that there was negligible rainfall.
Step 2
the mean of the Daily Total Rainfall in Camborne for August 2015.
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Answer
To calculate the mean, use the formula:
[ \mu = \frac{\sum r}{n} = \frac{174.9}{31} \approx 5.64 , \text{mm} ]
Step 3
the standard deviation of the Daily Total Rainfall in Camborne for August 2015.
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The standard deviation is calculated using the formula:
[ \sigma_r = \sqrt{\frac{\sum r^2}{n} - \mu^2} = \sqrt{\frac{3523.283}{31} - (5.64)^2} \approx 9.05 , \text{mm} ]
Step 4
State, giving a reason, whether this provides evidence to support Dian's belief.
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Answer
Dian's belief is not supported as the mean Daily Total Rainfall for Camborne is found to be 5.64 mm, while in Leuchars, it is 1.72 mm. This suggests that requirements of comparisons do not favor the hypothesis about rain being less in South than North, demonstrating that Leuchars experiences less rainfall.
Step 5
Explain why the distribution B(14, 0.27) might not be a reasonable model for the number of days without rain for a 14-day summer event.
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The distribution B(14, 0.27) assumes independence among days, which may not hold during summer months when weather patterns can affect multiple consecutive days. Furthermore, a probability of 0.27 indicates a relatively high chance of rain, making it unlikely that the count of days without rain would fit this model properly.
