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 2

To find the probability that cloud cover is less than 50%, we need to count the number of favorable outcomes. For values less than 50%, possible values are from 0% to 49%. This means there are 50 favorable outcomes (0, 1, 2, ..., 49), out of a total of 101 possible outcomes (0 through 100).

Thus, the probability is given by:

$P(C < 50) = \frac{50}{101} \approx 0.495$

Helen's model suggests that the probability of cloud cover being less than 50% is approximately 49.5%. However, data from 2015 indicates that the actual proportion of days with less than 50% cloud cover was 31.5%. This discrepancy suggests that the discrete uniform model may not be suitable as it overestimates the probability of low cloud cover days. Such a high probability in the model does not align with the observed data, indicating that real-world conditions may affect cloud cover distribution.

To refine Helen’s model, one could consider using a probability distribution that takes into account the empirical data. A beta distribution or a binomial distribution could be more appropriate as they can model the outcomes based on actual observations. Specifically, an empirical distribution based on historical data could provide a better fit by incorporating the observed proportions of cloud cover values.