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An HMO is considering a marketing plan targeting patients with chronic diseases to increase the number getting a flu shot

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An HMO is considering a marketing plan targeting patients with chronic diseases to increase the number getting a flu shot. Some preliminary analyses are conducted before implementing such a plan. Available data indicate that 40% of patients with chronic diseases get flu shots.

a)If 10 patients with chronic diseases are sampled, what is the probability that at least 4 get flu shots regularly?
b)What is the probability that at most 8 get flu shots regularly?

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a) This is a question of binomial probability, with p = 0.4, n = 10, x >= 4
P(X >= 4) = 1 - P(X <= 3) = = 1 - BINOMDIST(3,10,0.4,1) = 0.617719.

b) This is a question of binomial probability, with p = 0.4, n = 10, x <= 8
P(X <= 8) = 1 - BINOMDIST(8, 10, 0.4, 1) = 0.998322.