Question

Work the following problem in Excel

Patients arrive at the emergency room of Costa Valley Hospital at an average of 5 per day. The demand for emergency room treatment at Costa Valley follows a Poisson distribution. (a) Using Excel compute the probability of exactly 0, 1, 2, 3, 4, and 5 arrivals per day. (b) What is the sum of these probabilities, and why is the number less than 1?

Answer 1

(a)we have find the probability of exactly 0,1,2,3,4,5.

P(X=0)=5^0e^-5/0! =0.0067

P(X=1)=5^1e^-5/1! =5e^-5=0.0336

P(X=2)=5^2e^-5/2! =25e^-5/2=0.0842

P(X=3)=5^3e^-5/3! =125e^-5/6=0.1403

P(X=4)=5^4e^-5/4! =625e^-5/24=0.1754

P(X=5)=5^5e^-5/5! =3125e^-5/120=0.1754

(b)

sum of all these properties=0.6156

which is short of what one since X can take considerably more qualities like 6,7,8,9, and so on etc and each having a huge likelihood esteem is the number less than 1