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?
Contingency Table
A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.
Binomial Distribution
Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.
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?)
(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?
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