Chapter 3, Problem 116 Heart failure is due to either natural occurrences (87%)

Question

Chapter 3, Problem 116 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 15 patients will visit an emergency room with heart failure. Assume that causes of heart failure between individuals are independent. (a) What is the probability that three individuals have conditions caused by outside factors? (b) What is the probability that three or more individuals have conditions caused by outside factors? (c) What is the mean and standard deviation of the number of individuals with conditions caused by outside factors? Round your answers to three decimal places (e.g. 98.765). (a) The probability is (b) The probability is (c) The mean is , and the standard deviation is

Explanation / Answer

Solution:- Given that n = 15 , p = 13% = 0.13 ,q = 87% = 0.87

a) P(X = 3) = 15C3 * (0.13)3 * (0.87)12

= 0.188

b) P(X >= 3) = 0.308

c) mean = np = 15*0.13 = 1.95

sd =sqrt(npq) = sqrt(15*0.13*0.87) = 1.302

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