1. 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 Mechanics - Question 1 - 2018 - Paper 1

To find the probability that cloud cover is less than 50%, we consider the values of C that correspond to less than 4:

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

From the probability distribution:

$P(C < 4) = \frac{1}{9} + \frac{1}{9} + \frac{1}{9} + \frac{1}{9} = \frac{4}{9} \approx 0.444$

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

Helen's model assumes a discrete uniform distribution for cloud cover. Given that the actual proportion of days with cloud cover of less than 50% (0.315) is lower than the model's prediction (0.444), it suggests that the model is not accurately representing the real-world data. Therefore, the uniform model may not be suitable.

A more appropriate model could be a non-uniform distribution, as cloud cover may vary significantly based on seasonal and locational factors. Using a continuous distribution to model cloud cover instead of a discrete one might provide a better fit for the data.