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Given that a certain medical condition is found in 1 out of 1000 persons. For an...

Given that a certain medical condition is found in 1 out of 1000 persons. For an island with a population of 500, the distribution ?~?(500,0.001) could be used to describe the proportion of population that is infected with the condition.
(d) Assuming the above Binomial proportion is applicable for another island with a population of 5000, and by using an appropriate approximation, find:
(i) the expected number of persons with the condition
(ii) the probability that there will be more than 5 persons infected with the condition

(e) The random variable ? has a binomial distribution ?~?(11,?). Given that ?(? = 8) = ?(? = 7). Show that ? = 2/3 .

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