question archive Heart failure is due to either natural occurrences (87%) or outside factors (13%)
Heart failure is due to either natural occurrences (87%) or outside factors (13%)
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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.
A. What is the probability that three individuals have conditions caused by outside factors?
B. What are the mean and standard deviation of the number of individuals with conditions caused by outside factors?
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Answer:
n = 20
a) prob that 3 individuals have conditions caused by outside factors = 20C3 * 0.133 * 0.8717 = 0.2347
b) p, = 0.13
P(X = 0) = 20C0 * 0.130 * 0.8720 = 0.0617
P(X = 1) = 20C1 * 0.131 * 0.8719 = 0.1844
P(X = 2) = 20C2 * 0.132 * 0.8718 = 0.2618
similarly, P(X = 3) = 0.2347
P(X = 4) = 0.1491
P(X = 5) = 0.0713
P(X = 6) = 0.0266
P(X = 7) = 0.007957
P(X = 8) = 0.001932
P(X = 9) = 0.00038495
P(X = 10) = 0.0000632739
P(X = 11) = 0.000008595201
P(X = 12) = 9.63255e-7
P(X = 13) = 8.8575e-8
P(X = 14) = 6.618e-9
P(X = 15) = 3.96e-10
P(X = 16) = 1.8e-11
P(X = 17) = 0
P(X = 18) = 0
P(X = 19) = 0
P(X = 20) = 0
var(X) = E(X2) - (E(X))2 = 9.022 - 2.62 = 2.262
std dev = sqrt(2.262) = 1.504
