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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
Step 2
Step 3
the standard deviation of the Daily Total Rainfall in Camborne for August 2015
Answer
The standard deviation can be calculated using the formula:
σ = rac{ ext{sqrt}( ext{Total } r^2 - rac{( ext{Total } r)^2}{n})}{n}Substituting the known values:
σ = rac{ ext{sqrt}(3523.283 - rac{(174.9)^2}{31})}{31} ightarrow σ ext{ is approximately } 9.05 ext{ mm}Step 4
State, giving a reason, whether this provides evidence to support Dian's belief.
Answer
Since the mean Daily Total Rainfall in Leuchars (1.72 mm) is less than that in Camborne (approximately 5.64 mm), it supports Dian's belief that the mean Daily Total Rainfall in the South is less than in the North, as Leuchars is located in the North and Camborne in the South.
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.
Answer
The distribution B(14, 0.27) assumes independence of events, which may not hold true for weather. Additionally, the probability of rain being constant (0.27) may not reflect the likelihood of consecutive rainy days, leading to an unreliable model in capturing the variability of summer rainfall.