when an opinion poll calls residential telephone numbers at randomonly 20% of th

Question

when an opinion poll calls residential telephone numbers at randomonly 20% of the calls reach a live person . You watch the randomdigit dialing machine make 15 calls. What is the mean number ofcalls that reach a person? What is the standard deviation of thecount of calls that reach a person? If the calls are made to NewYork City rather than nationally, the probability a call reaches aperson is only p=0.08. How does this new P effect the standarddeviation? What would be the standard deviation if P=0.01? whatdoes your work show about the behavior of the standard deviation ofbinomial distribution as the probability of success gets closer to0?

Explanation / Answer

Given X~Binomial(n=15, p=0.2) The mean number of calls that reach a person is n*p= 15*0.2 = 3 The standard deviation of the count of calls that reach a personis n*p*(1-p) = 15*0.2*0.8 =1.549 E(X) = 0.08*15 = 1.2 V(X) = 1.2*0.92 = 1.104 SD = 1.0507 E(X) = 0.01*15 = 0.15 V(X) = 0.15*0.99 = 0.1485 SD = 0.3854

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