Arrival at a focal emergency department on Tuesday nights have been found to fol

Question

Arrival at a focal emergency department on Tuesday nights have been found to follow Poisson distribution with a parameter of 13 arrivals per hour. Use the above scenario to answer the follow questions a. What is the probability that the hospital will receive exactly 10 arrivals in a even hour (on a Tuesday night)? b. What is the probability that the hospital will receive less than 10 arrivals in a given hour (on a Tue night)? c. What is the probability that the hospital will receive between 11-13 arrivals in a given hour (on a Tuesday night)? What is the probability that the hospital will receive more than 4 arrivals in a given hour (on a Tuesday night)? e. You can't create a distribution table for all values of the random variable like you did for question #1 of this section. Why not?

Explanation / Answer

Here = 13 arrivals per hour

a. Pr (x = 10; 13) = x e- /x!

Pr (x = 10; 13) = (13) 10 e-13/10! = 0.08587

b. Pr (X< 10; 13) = we will calculate it by poission distribution calculator

Pr (X< 10; 13) = 0.1658

c.Pr( X =11,12,13; 13) = Pr( X=11) + Pr( X =12) + Pr( X =13)

= 0.1014 + 0.1100 + 0.1100 = 0.3214

d. P (X>=4 ; 13) = 1 - P( X<=4; 13) = 1- 0.02925 = 0.97075

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