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

To find the probability that cloud cover is less than 50%, we consider the values of C that are less than 4, which are 0, 1, 2, and 3. Thus:

$P(C < 4) = P(C = 0) + P(C = 1) + P(C = 2) + P(C = 3) = 4 \cdot P(C = c) = 4 \cdot \frac{1}{9} = \frac{4}{9} \approx 0.444$

So, the probability that cloud cover is less than 50% is approximately 0.444.

The model shows the probability of cloud cover being less than 50% is approximately 0.444, while Helen found this proportion to be 0.315 in 2015. Since 0.444 is higher than 0.315, this suggests that the uniform distribution is not accurately capturing the actual distribution of cloud cover data. This discrepancy indicates that the model might not be suitable, as it predicts a probability that is significantly higher than observed.

To refine Helen's model, it would be beneficial to consider a non-uniform distribution that better reflects the variations in cloud cover over time and location. For example, a continuous model, like a normal distribution, could capture the observed probabilities more accurately by incorporating seasonal variations and other influencing factors. Additionally, using historical data to find the mean and standard deviation of cloud cover could provide a more precise model.