Heart failure is due to either natural occurrence (87%) or outside factors (13%)

Question

Heart failure is due to either natural occurrence (87%) or outside factors (13%). Outside factors are related to induced substances or foreign objects. Natural occurrences are caused by arterial blockage, disease, and infection. Suppose that 20 patients will visit an emergency room with heart failure. Assume that causes of heart failure for the individuals are independent. What is the probability that three individuals have conditions caused by outside factors? What is the probability that three or more individuals have conditions caused by outside factors? What are the mean and standard deviation of the number of individuals with conditions caused by outside factors?

Explanation / Answer

a) P(x=3)=20C3*(0.13)^3 (0.87)^17 =0.2347

b) P(x>=3)=1-[P(x=0)+P(x=1)+P(x=2)]=0.492

c) mean is 20*0.13 =2.6 and variance is 20*(0.13)*(0.87)=2.262

and standard deviation is sqaure root of variance i,e 1.5039

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