Osteoporosis is a condition in which the bones become brittle dueto loss of mine

Question

Osteoporosis is a condition in which the bones become brittle dueto loss of minerals. To diagnose osteoporosis, an elaborateapparatus measures bone mineral density (BMD). BMD is usuallyreported in standardized form. The standardization is based on apopulation of healthy young adults. The World Health Organization(WHO) criterion for osteoporosis is a BMD 2.5 standard deviationsbelow the mean for young adults. BMD measurements in a populationof people similar in age and sex can be approximated quite wellwith a normal model.

a. What percent of healthy young adults have osteoporosis bythe WHO criterion?
b. Women aged 70 to 79 are of course not young adults. The mean BMDin this age is about -2 on the standard scale for young adults.Suppose that the standard deviation is the same as for youngadults. What percent of this population has osteoporosis?(NOTE that on the standardized scale for young adults the standarddeviation is 1).

Explanation / Answer

a. The probability of being 2.5 standard deviations below the meancan be found by reading a standard normal table at 2.50, which isgiven to be 0.9938. Since the table is symmetric, 1 - 0.9938 =0.62% of young adults are predicted to have osteoporosis. b. Reading the table in the same manner, the probability of beingto the left of 2.0 is 0.9773. Again given the symmetry, this meansthat 97.73% of women aged 70 to 79 are predicted to haveosteoporosis.

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