d. 0.855 Part II 1. (O pts.), On weekend nights, a large urban hospital has an a

Question

d. 0.855 Part II 1. (O pts.), On weekend nights, a large urban hospital has an average of 3,.6 emergency arrivals per hour. Let X be the number of arrivals per hour on a weekend night at this hospital. Assume that successive arrivals are random and independent. (a) What is the distribution of X? .8 73 L3.6 O 1.8973 (b)What is the probability of observing exactly three emergency arrivals? (c) What is the probability of observing more than two emergency arrivals? 2.(8 pts.) The distribution of total body protein in adult men with liver cirrhosis is approximately Normal with mean 10.3 kg and standard deviation 0.2 kg.

Explanation / Answer

a)

X~ poisson

If is the average number of successes occurring in a given time interval or region in the Poisson distribution, then the mean and the variance of the Poisson distribution are both equal to .

E(X) =

and

V(X) = 2 =

= 3.6

b)

Poisson's Distribution Formula:

P(X)= e^ * ^x/x!

P(X = 3) = (e^-3.6) (3.6^3) / 3! = 0.1687

= 0.2125

c)

P(X >2) = 1 - p(X < =1)

= 1 - P(X = 0) + P(X = 1)+ P(X=2)

= 1 - (e^-3.6) (3.6^0) / 0! + (e^-3.6) (3.6^1) /1! + (e^-3.6) (3.6^2) / 2!

= 0.6973

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