The maternity ward of a large London-based hospital trust has signed a contract with the National Health Service to deliver 13000 babies in 2021. To achieve this, it needs to have approximately 250 deliveries per week (=13000 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 250 deliveries were scheduled, approximately 14% of the booked deliveries did not show up, but this number varies from week to week - it could be as low as 8% or as high as 20%.

1. (5 points) 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.

Binominal distribution to provide us with a yes or no distribution.

Given the 14% no-show rate, it has been argued that if the hospital wants to meet the target of 13000 deliveries per year, it will need to book an additional 14% deliveries, i.e, instead of booking 250 deliveries per week it will need to book 285 (an extra 35 =14%*250 bookings per week). This will ensure that it will not miss the 13000 deliveries target.

1. (5 points) What do you think of this reasoning?

The reasoning is incorrect because we are not taking into account the no show rate of the aThe maternity ward of a large London-based hospital trust has signed a contract with the National Health Service to deliver 13000 babies in 2021. To achieve this, it needs to have approximately 250 deliveries per week (=13000 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 250 deliveries were scheduled, approximately 14% of the booked deliveries did not show up, but this number varies from week to week - it could be as low as 8% or as high as 20%.

1. (5 points) 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.

1. (5 points) How would you build a simulation model to estimate the probability of achieving the 13000 births target if the number of deliveries booked per week is 291?