Helen believes that the random variable C, representing cloud cover from the large data set, can be modelled by a discrete uniform distribution - Edexcel - A-Level Maths Statistics - Question 1 - 2018 - Paper 2

In the context of the problem, cloud cover values less than 50% correspond to values of C from 0 to 4 (assuming 0 corresponds to 0% and 8 corresponds to 100%). Thus, we have:

$P(C < 4) = P(C=0) + P(C=1) + P(C=2) + P(C=3) + P(C=4)$

Since there are five values (0, 1, 2, 3, 4), the probability is:

$P(C < 4) = 5 \times \frac{1}{9} = \frac{5}{9} \approx 0.555$

Helen's model suggests that the expected probability of cloud cover being less than 50% is approximately 0.555. However, the actual proportion observed in Hurn for 2015 was 0.315, which is significantly lower. This indicates that the discrete uniform model may not be appropriate since it overestimates the probability of low cloud cover days. The model does not accurately reflect the variability inherent in actual weather patterns.

A more suitable model might involve considering non-uniform distributions to account for different weather patterns and locations. For instance, a model that adjusts the probabilities based on historical data could better capture the variations in cloud cover. Moreover, using a continuous model could also be considered to provide a more realistic representation of cloud cover.