11. Heart failure is due to either natural occurrences (87%) or outside factors (13%). Outside factors...

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11. 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 between individuals are independent. (Show all Octave commands and output.) a. What is the probability that three individuals have conditions caused by outside factors? P(X = 3) = (20) (0.13) (1 -0.13) 20-3 = 1140 x 0.002 x 0.0937 = 0.2347 b. What is the probability that three or more individuals have conditions caused by outside factors? P(X3) 1 P(X < 3) 1-(P(X = 0) + P(X = 1) + P(X = 2)) 1-[(20) (0.13)(1 -0.13) 20-0 + (20) (1 0.13) 20-1 + (20) (0.13)(1 0.13) 20-2] 1 (0.0617 +0.1844 + 0.2618) = 0.4921 - c. What are the mean and standard deviation of the number of individuals with conditions caused by outside factors? = np 20 x 0.13 = 2.6 - = mp(1 - p20 0.13(1 0.13) = 1.504 d. Assume that one evening the emergency room sees 20 patients with heart failure. Is it very likely that 10 would be due to outside factors? Explain. 11. 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 between individuals are independent. (Show all Octave commands and output.) a. What is the probability that three individuals have conditions caused by outside factors? P(X = 3) = (20) (0.13) (1 -0.13) 20-3 = 1140 x 0.002 x 0.0937 = 0.2347 b. What is the probability that three or more individuals have conditions caused by outside factors? P(X3) 1 P(X < 3) 1-(P(X = 0) + P(X = 1) + P(X = 2)) 1-[(20) (0.13)(1 -0.13) 20-0 + (20) (1 0.13) 20-1 + (20) (0.13)(1 0.13) 20-2] 1 (0.0617 +0.1844 + 0.2618) = 0.4921 - c. What are the mean and standard deviation of the number of individuals with conditions caused by outside factors? = np 20 x 0.13 = 2.6 - = mp(1 - p20 0.13(1 0.13) = 1.504 d. Assume that one evening the emergency room sees 20 patients with heart failure. Is it very likely that 10 would be due to outside factors? Explain.