Bone density. Forty percent of postmenopausal women have low bone density (osteopenia), placing them at risk for osteoporosis with ensuing spontaneous fractures. Osteoporosis is estimated to lead to $14 billion per year in medical expenses alone, yet it can be prevented if treated early enough. A physician group has 248 postmenopausal primary patients and has diagnosed 82 of these women with low bone density. What is the probability that only 82 or fewer of a set of 248 patients have low bone density? Use the Normal approximation to find this probability. Find the probability in part a using the binomial probability model. How does it compare with the Normal approximation? Based on the probability of this outcome, what would you suggest at the next physicians meeting?

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 Bone density. Forty percent of postmenopausal women have low bone density (osteopenia), placing them at risk for osteoporosis with ensuing spontaneous fractures. Osteoporosis is estimated to lead to $14 billion per year in medical expenses alone, yet it can be prevented if treated early enough. A physician group has 248 postmenopausal primary patients and has diagnosed 82 of these women with low bone density.

    1. What is the probability that only 82 or fewer of a set of 248 patients have low bone density? Use the Normal approximation to find this probability.
    2. Find the probability in part a using the binomial probability model. How does it compare with the Normal approximation?
    3. Based on the probability of this outcome, what would you suggest at the next physicians meeting?
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