Assume that a specific emergency department has a length of stay with behavior n

Question

Assume that a specific emergency department has a length of stay with behavior normally distributed; mean of 5 hours and a standard deviation of 3 hours. Use standard normal random variables to resolve these probabilities. (a) What is the probability of a length of stay greater than 12 hours? (b) What length of stay is exceeded by 20% of the visits? (c) From the normally distributed model, what is the probability of a length of stay less than 0 hours? Comment on the normally distributed assumption in this example.

Explanation / Answer

here mean=5 and sd=3.

we use standard normal variate z=(x-mean)/sd

x=length of stay

(a) P(x>12)=P(z>2.333)=1-P(z<2.333)=1-0.99=0.01

P(z<2.333)=0.01 (using ms-excel command =normsdist(2.333))

for x=12, z=(12-5)/3=7/3=2.333

(b) first we find z1 , so that P(z>z1)=0.2 or P(z<z1)=1-0.2=0.8 and z1=0.8416

and corresponding x value is given as

x=5+3*0.8416=7.5248

(c) P(x<0)=P(z<-1.667)=0.0477

for x=0, z=(0-5)/3=-1.667

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