The maternity ward of a large London-based hospital trust has signed a contract with the National Health Service to deliver 14000 babies in 2021. To achieve this, it needs to have approximately 270 deliveries per week (=14000 deliveries/52 weeks). Deliveries are booked when the expecting mother is towards the end of the first trimester of gestation (i.e., about 6 months before they actually take place). However, one concern is the phenomenon of no-shows - women who book but never show up to deliver. This happens for a number of reasons, e.g., the mother moves out of London, experiences a miscarriage, etc. In the past, on weeks where 270 deliveries were scheduled, approximately 12% of the booked deliveries did not show up, but this number varies from week to week - it could be as low as 6% or as high as 18%.

What would be a good distribution to choose to model the number of mothers booked per week who do not show up to deliver? Justify your choice.

Given the 12% no-show rate, it has been argued that if the hospital wants to meet the target of 14000 deliveries per year, it will need to book an additional 12% deliveries, i.e, instead of booking 270 deliveries per week it will need to book 303 (an extra 33 =12%*270 bookings per week). This will ensure that it will not miss the 14000 deliveries target.

What do you think of this reasoning?

How would you build a simulation model to estimate the probability of achieving the 14000 births target if the number of deliveries booked per week is 307?