Osteoporosis Postmenopausal
Mar/060
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39% of postmenopausal women have low bone density (osteopenia), placing them at risk for osteoporosis with ens?
39% of postmenopausal women have low bone density (osteopenia), placing them at risk for osteoporosis with ensuing spontaneous fractures. Osteoporosis is estimated to cost $14 billion per year in medical expenses alone, and yet it can be prevented if treated early enough. A physicians group has 249 postmenopausal primary patients and has diagnosed 81 with low bone density.
(a) What is the probability that only 81 or fewer of the 249 patients have low bone density? Find the probability using the binomial probability model
(b) Find the probability in (a) using the Normal approximation to the binomial distribution.
qa
binomial probability model
n = 249 , p = 0.39 , q = 0.61
P[k] = nCk*p^k*q^(n-k)
P[<=81] = P[0] + P[1] + ... + P[81]
using a binomial calculator, P[<=81] = 0.0204 or 2.04 %
qb
for the normal approximation to the binomial distribution,
mean = np = 97.11, SD = sqrt(npq) = 7.697
applying the continuity correction
for using a continuous distribution
for a discrete distribution,
<= 81 becomes <= 81.5
z value = [81.5 - 97.11] / 7.697 = - 2.03
reqd. probability = 0.0212 or 2.12 %
Post-menopausal osteoporosis awareness for International Women's Day 2009
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