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

To calculate the mean Daily Total Rainfall, we can use the formula:

$$ar{x} = rac{ extstyle extstyle extstyle extstyle extstyle extstyle extstyle extstyle extstyle extstyle extstyle extstyle extstyle extstyle extstyle extstyle extstyle extstyle extstyle extstyle extstyle extstyle extstyle extstyle extstyle extstyle extstyle extstyle extstyle extstyle extstyle extstyle extstyle extstyle extstyle extstyle extstyle extstyle extstyle extstyle extstyle extstyle extstyle extstyle extstyle extstyle extstyle extstyle extstyle { extstyle= extstyle= extstyle= extstyle= extstyle= extstyle= extstyle extstyle extstyle 174.9}{31} = 5.64$ mm.

The standard deviation can be calculated using the formula:

ext{s} = rac{ ext{squared sum of residuals}}{n - 1}

where the squared sum is given by ext{Var} = rac{3532.283}{31} - (5.64)^2 \approx 9.19

Thus, $ext{s} = ext{sqrt}(9.19) ext{ which is approximately } 3.02$ mm.

Dian's belief is that the daily rainfall in the south is less than in the north. Observing that Leuchars has a mean rainfall of 1.72 mm suggests the mean rainfall in the south is indeed lower than the mean in Camborne (5.64 mm), but the evidence is not definitive as local variations can occur. Therefore, while it does provide some support, it is not conclusive.

The binomial distribution B(14, 0.27) relies on the assumption that each day is an independent trial with the same probability of no rain, which might not hold in a summer period. Weather patterns may create dependencies between consecutive days, and the probability $0.27$ itself may not accurately reflect the daily likelihood for specific local conditions in summer.