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
Write down 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, a value of 0 < r ≤ 0.05 is recorded in the category representing 'trace' rainfall. This indicates minimal rainfall that is not focused in the usual increments.
Step 2
the mean of the Daily Total Rainfall in Camborne for August 2015.
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Answer
To calculate the mean Daily Total Rainfall (
μ
), we use the formula:
μ=nΣr=31174.9≈5.64516.
Therefore, the mean Daily Total Rainfall in Camborne for August 2015 is approximately 5.64 mm.
Step 3
the standard deviation of the Daily Total Rainfall in Camborne for August 2015.
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Answer
The standard deviation (
σ
) can be found using the formula:
σ=nΣr2−μ2=313523.283−(5.64516)2≈0.9456.
Thus, the standard deviation of the Daily Total Rainfall in Camborne for August 2015 is approximately 0.95 mm.
Step 4
State, giving a reason, whether this provides evidence to support Dian's belief.
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Answer
Leuchars is in the North and Camborne is in the South. Since the mean Daily Total Rainfall for Leuchars is 1.72 mm, which is significantly less than that for Camborne (approximated to be 5.64 mm), this comparison suggests that the rainfall in the North is lower than in the South. Therefore, there is insufficient evidence to support Dian's belief.
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 and a constant probability of rain each day. However, during a summer event, weather patterns can be influenced by atmospheric conditions that may not align with this assumption. Therefore, the probability of having rain on different days may vary, making this model less suitable.
