Question

Patients arrive at the emergency room of Costa Val- ley Hospital at an average of 5 per day. The demand for emergency room treatment at Costa Valley fol- lows a Poisson distribution. (a) Using Appendix C , What is the sum of these probabilities, and why is the number less than 1?

The Appendix C, compute the probabilty of exactly 0,1,2,3,4, and 5 arrivals per day. Put in excel.

Answer 1

Formula sheet

A	B	C	D	E	F	G	H	I	J
2
3		As per Poisson distribution, the probability of observing k events over time is
4		P(X=k) = (?ke-?)/k!
5
6		Where ? is the average number of times the event occurs over the time period.
7
8		Since number of patient arriving the energency room is 5 per day,
9		therefore ? is 5 per day and period is day.
10
11		?=	5	per day
12
13		As per Poisson distribution, the probability of observing k arrivals per day will be
14		P(X=k)	= (?ke-?)/k!
15
16		P(X=0)	= (?0e-?)/0!
17			=POISSON.DIST(0,D11,FALSE)	=POISSON.DIST(0,D11,FALSE)
18
19		Hence probability of zero arrivals per day is	=D17
20		Similarly probability of other number of arrivals can be calculated as below:
21
22		P(X=1)	= (?1e-?)/1!
23			=POISSON.DIST(1,$D$11,FALSE)	=POISSON.DIST(1,$D$11,FALSE)
24
25		P(X=2)	= (?2e-?)/2!
26			=POISSON.DIST(2,$D$11,FALSE)
27
28		P(X=3)	= (?3e-?)/3!
29			=POISSON.DIST(3,$D$11,FALSE)
30
31		P(X=4)	= (?4e-?)/4!
32			=POISSON.DIST(4,$D$11,FALSE)
33
34		P(X=5)	= (?5e-?)/5!
35			=POISSON.DIST(5,$D$11,FALSE)
36