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 need to identify the values of $C$ that correspond to less than 50%. Assuming that values 0 through 4 represent cloud cover percentages less than 50%, we can count these values. Thus, we have:

• Values less than 4: 0, 1, 2, 3
• This gives us 4 favorable outcomes.

The probability is then calculated as follows:

$P(C < 4) = \frac{4}{9}$

Helen's model predicted that the probability of cloud cover being less than 50% was $\frac{4}{9} \approx 0.444$. However, the actual proportion from the data set is 0.315. This indicates that the model overestimates the probability of low cloud cover days. Since the calculated probability is higher than the observed proportion, we infer that a uniform distribution may not be suitable. The underlying conditions affecting cloud cover may vary significantly, thus suggesting the need for a more tailored model.

A suitable refinement to Helen's model could involve using a non-uniform distribution. Factors such as geographical location and seasonal changes often influence cloud cover. A model that allocates different probabilities to the days based on these factors would likely provide a more accurate representation of actual cloud cover data.