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Age group, years Percent of office visitors Under 15 15-24 25-44 45-64 65 and older 20% 10% 25% 20% 25% Suppose you are a district manager of a health management organization (HMO) that is monitoring the office of a local doctor or nurse in general family practice. This morning the office you are monitoring has eight office visits on the schedule. What is the probability that (a) at least half of the patients are under 15 years old? First explain how this can be modeled as a binomial distribution with 8 trials, where success is visitor age is under 15 years old and the probability of success is 20%. (b) (c) (d) (e) n=8, p=0.20, q=0.80, r≥4 P(r≥4) = P(4) + P(5) + P(6) + P(7) + P(8) =0.0562816 from 2 to 5 patients are 65 years old or older (include 2 and 5)? P(2≤r≤5) = P(2) + P(3) + P(4) + P(5) = 0.628692625 from 2 to 5 patients are 45 years old or older (include 2 and 5)? Hint: Success is 45 or older. Use the table to compute the probability of success on a single trial. 45%? all the patients are under 25 years of age? 30%? all the patients are 15 years old or older? 80%?