Heart failure Is due to either natural occurrences (87%) or outside factors (13%

Question

Heart failure Is due to either natural occurrences (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. Assume that causes of heart failure for the individuals are independent. What is the probability that three or more individuals have conditions caused by outside factors? 0.342 0.492 0.272 0.692 What is the mean of the number of individuals with conditions caused by outside factors? 2.6 1.9 3.0 5.8 What is the standard deviation of the number of individuals with conditions caused by outside factors? 3.982 2.262 1.504 1.995

Explanation / Answer

A)The random variable X follows binomial distribution with parameters n=20, p=0.13.

Find P(X>=3)

=P(X=3)+…+P(X=20)

=20C3*0.13^3*0.87^17+…+20C20*0.13^3*0.87^0

=0.492

B)The mean number of individuals with conditions caused by outside failures is:

N*p=20*0.13

=2.6

C)The standard deviation of individuals with conditions caused by outside failures is:

Root over Np(1-p)

=root over 2.6*0.87

=1.503

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