42% 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 80 with low bone density. (a) What is the probability that only 80 or fewer of the 249 patients have low bone density? Find the probability using the binomial probability model. Use the =binom.dist(k,n,p,cumulative?) function in Excel. Use 4 decimal places. (b) Find the probability in (a) using the Normal approximation to the binomial distribution. Use 4 decimal places. (c) Based on your answer to the previous problem, what would you suggest at the next physicians meeting?

42% 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 80 with low bone density.

(a) What is the probability that only 80 or fewer of the 249 patients have low bone density? Find the probability using the binomial probability model. Use the =binom.dist(k,n,p,cumulative?) function in Excel. Use 4 decimal places.

(b) Find the probability in (a) using the Normal approximation to the binomial distribution. Use 4 decimal places.

(c) Based on your answer to the previous problem, what would you suggest at the next physicians meeting?