It is believed that the number of emergency room visits on Friday nights at hosp

Question

It is believed that the number of emergency room visits on Friday nights at hospitals follows a Poisson distribution with = 12. Suppose that 30 Friday nights are sampled and the number of emergency room visits (X) are recorded at a particular hospital.

(a) The hospital administration will conclude that the ER is seeing fewer patients than other hospitals if X < 11. Use the central limit theorem to approximate the probability that this conclusion is made when, in reality, the hospital is not different from the general population of hospitals. What type of error occurs if this conclusion is made?

(b) Actually, the number of ER visits on Friday nights does not follow a Poisson distribution but instead follows an unknown distribution with = 12 and = 5. Using the central limit theorem, re-compute the probability found in (a).

Explanation / Answer

a) here mean =12 and std eerror of mean for sample size n=30 =std deviation/(n)1/2 =(12/30)1/2 =0.6325

therefore P(X<11) =P(Z<(11-12)/0.6325)=P(Z<-1.5811)=0.0569

b) here from above data : std error of mean =5/(30)1/2 =0.9129

therefore P(X<11) =P(Z<(11-12)/0.9129)=P(Z<-1.0954)=0.1367

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