Resulting distribution used by Ofqual (green + orange - yellow):
This highlights one problem in the system - that the core maths is wrong. There are many others!
Where there are negative probabilities in the output Ofqual distribution these are the result of their equation. In practise (Annex E, X7, of requirements document) Ofqual moves the probability mass from negative probabilites to their neighbours.
In practise the standard deviations will be very wide, but the problem is much more obvious if they are set low.
This is assuming a large cohort size, as it ignores the small cohort logic.
This is assuming that GCSE results are available for all students.
2019 should be interpreted as the average over the last two or three years.