A medical test will be positive for 0.05% of people and negative for everyone else. Suppose a hospital will test 4000 patients each day. Use an appropriate approximation to find the probability that 5 people test positive tomorrow. (5SF)
Note that we have a constant probability, fixed number of tests, independent patients and only two outcomes, so we can write a binomial distribution X~Bin(4000,0.0005) where X is the random variable representing the number of patients who test positive.Use a Poisson approximation with L=np=2, so P(X=5) = ~(e^(-2)2^5)/5! = 0.036089
JM
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