Question 1
Paper 1Hard6 marksA local emergency department records two types of admissions during each 20-minute interval. The two streams of admissions are independent, and admissions occur independently at a uniform average rate throughout each interval. The mean numbers are 1.4 type A admissions and 0.9 type B admissions per interval.
A planner is considering a normal, binomial or Poisson model for the total number, of admissions in an interval.
Show that a suitable model for is a Poisson distribution with mean 2.3.
The department can assess at most admissions during an interval. The planner requires the probability that the department can assess all admissions to be at least 0.95.
Using your model from part (a), determine the smallest possible integer value of Show numerical evidence that it is the smallest value satisfying the requirement.