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March 25, 2017

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A drug is essential to the profileration of lymphocytes can cause kidney damage in 1% of patients. If the drug is given to 30 patients, find:

A)the probability exactly 1 patient suffers kidnay damage

B)the probabaility that less than 2 patients suffer kidney damage

c) the probability that at least 3 patients suffer kidney damage

d) the expected # of people who will suffer kidney damage

e) the standard deviation of the number of people who will suffer kidney damage

  • statistics - ,

    p = .01

    binomial distribution, n = 30

    A)
    p(k) = C(30,k) p^(k) p^(30-k)
    for k = 1
    p(1) = [30!/(1!29!)]* .01^1 * .99^29
    = 30*.01*.747
    =.224

    B)
    That would be zero or one patient. We know p(1) = .224 so find p(0)
    p(0) = (30!/0!30!) *.01^0 * .99^30
    = 1 * 1 * .740
    =.740
    so the probability of less than 3 is .224+.740 = .964

    C. 1-.964 = 0.036


    D. mean = n p = 30*.01 = 0.3

    E. variance = n p(1-p) =30*.01*.99 = .297
    s = sqrt(.297) = .545

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