a) To find out what is the probability that only 82 or fewer of a set of 248 patients have low bone density. b) To find the probability in part (a) using the binomial probability model and how does it compare with the normal approximation. c) To explain what would you suggest at the next physicians meeting based on the probability of this outcome.

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a) To find out what is the probability that only 82 or fewer of a set of 248 patients have low bone density.  b) To find the probability in part (a) using the binomial probability model and how does it compare with the normal approximation.  c) To explain what would you suggest at the next physicians meeting based on the probability of this outcome.

Alix Ortiz · Accepted Answer

a) It is given in the question that forty percent of postmenopausal women have low bone density. Thus, it has binomial distribution i.e. X∼B∈(248,0.4) Thus, the probability that only 82 or fewer of a set of 248 patients have low bone density can be calculated by using normal approximation. So, first we have to calculate the mean and standard deviation as: Mean=np =248×0.4 =99.2 St. Dev. =npq =248×0.4×0.6 =7.715 This implies, X∼N(99.2,7.715) Thus, the probability is as: P(X≤82)=P(Z≤82−99.27.715) =P(Z≤−2.23) =1−P(Z&amp;lt;2.23) =1−0.98713 =0.01287 b) It is given in the question that forty percent of postmenopausal women have low bone density. Thus, it has binomial distribution i.e. X∼B∈(248,0.4) So, to calculate the probability in part (a) using the binomial probability model we will be using the excel function for binomial distribution as: =BINOM.DIST(numbers, trials, prob, cumulative) Thus, we have, P(X&amp;lt;82)=BINOM.DIST(82,248,0.4,TRUE) And the result is as: P(X&amp;lt;82)=0.014485 So, the probability calculation using normal approximation is fairly near to the probability calculated using the binomial probability. c) It is given in the question that forty percent of postmenopausal women have low bone density. Thus, it has binomial distribution i.e. X∼B∈(248,0.4) SInce after postmenopausal women have low bone density, which place them at risk for osteoporosis with ensuing spontaneous fractures. Since the probability is not very high so we can say that most of the cases of women for osteoporosis were missed.

a) To find out what is the probability that only 82 or fewer of a set of 248 pat

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