Question

-9 Based on her experience, a hospital administrator feels that 5% of all newly admitted patients must be put immediately into intensive care. Use this figure to estimate the probability that among 120 newly admitted patients, three will have to be put immediately into intensive care.

Answer 1

Let , X be the number of admitted patients must be put immediately into intensive care.

Here , $X\to B(n=120,p=0.05)$

Here , n=120>20 and p$\leq$0.05

Therefore , use the Poisson approximation with parameter $\lambda=np=120*0.05=6$

Now , we want to find the P(X=3)

$P (X=3)=\frac{e^{-6}6^3}{3!}=0.0892$

Therefore , the probability that among 120 newly admitted patients , three will have to be put immediately into intensive care is 0.0892