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    Binomial Distribution: Infectious and Pulmonary Disease

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    1. Infectious disease question:
    Evaluate the probabilities of obtaining k neutrophils out of 5 cells for k=0,1,2,3,4,5 where the probability that any one cell is a neutrophil is 0.6. Find the expected number and standard deviation of neutrophils of the 5 cells.

    2. Pulmonary disease question:
    Compute the probability of obtaining exactly 7 cases of chronic bronchitis and the probability of obtaining at least 7 cases of chronic bronchitis in the first year among 10 families, where both parents have chronic bronchitis, if the underlying incidence rate of chronic bronchitis in the first year of life is 0.05.

    3. Use normal approximation to Binomial distribution, to compute the probability of at least 75 cases of chronic bronchitis in the first year among 1500 families for the pulmonary disease.

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    Solution Preview

    Please see the attached file for the complete and formatted solution.

    4. The number of neutrophils follows a binomial(5, 0.6) distribution. This distribution has a probability mass function of:
    Plugging in each of the values ...

    Solution Summary

    This solution goes through the different uses of the binomial distribution using different examples: infectious disease, pulmonary disease, as well as the normal approximation to the binomial distribution.

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