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 find the mean of the Daily Total Rainfall, we use the formula:

ar{x} = rac{ ext{Σr}}{n}

Substituting the values:

ar{x} = rac{174.9}{31} \\ ar{x} \\ ext{Mean} \\ = 5.641 ext{ mm (awrt 5.64 mm)}

The formula for the standard deviation is:

ext{s} = rac{ ext{sqrt(Σr² - }rac{( ext{Σr})^2}{n})}{n - 1}

First, we calculate (Σr² - \frac{(Σr)^2}{n}):

$3523.283 - \frac{(174.9)^2}{31} = 3523.283 - 1009.903 \\ = 2513.38$

Then, the standard deviation is:

$s = \sqrt{\frac{2513.38}{31 - 1}} = \sqrt{\frac{2513.38}{30}} \approx 9.04559 ext{ mm (awrt 9.05 mm)}$

Leuchars is in the North and Camborne is in the South. The recorded mean Daily Total Rainfall for Leuchars (1.72 mm) is less than that for Camborne (calculated mean 5.64 mm). Thus, there is no evidence to support Dian's belief that the mean Daily Total Rainfall in August is less in the South than in the North of the UK.

The B(14, 0.27) distribution assumes independence between days of rainfall. However, if the weather conditions are not independent, such as prolonged rainy seasons or specific climatic conditions affecting the 14-day period, this model may not hold. Additionally, the probability of rain not being a constant 0.27 could lead to inaccuracies.