2 points MBasicStat7 15.E.029 My Notes Ask Your Teacher Shelia\'s doctor is conc

Question

2 points MBasicStat7 15.E.029 My Notes Ask Your Teacher Shelia's doctor is concerned that she may suffer from gestational diabetes (high blood glucose levels during pregnancy). There is variation both in the actual glucose level and in the blood test that measures the level. In a test to screen for gestational diabetes, a patient is classified as needing further testing for gestational diabetes if the glucose level is above 130 milligrams per deciliter (mg/dL) one hour after a sugary drink. Shelia's measured glucose level one hour after the sugary drink varies according to the Normal distribution with 115 mg/dL and 14 mg/dL. (Round your answers to four decimal places.) (a) If a single glucose measurement is made, what is the probability that Shelia is diagnosed as having gestational diabetes? (b) If measurements are made on three separate days and the mean result is compared with the criterion 130 mg/dL, what is the probability that Shelia is diagnosed as needing further testing for gestational diabetes?

Explanation / Answer

solution=

If a single glucose measurement is made, what is the probability (±0.0001) that Shelia is diagnosed as having gestational diabetes?

z = 130 115 / 14 =1.0714286

P(x >130) = P(z >1.0714286) = 0.8580

If measurements are made on 3 separate days and the mean result is compared with the criterion 130 mg/dl, what is the probability (±0.0001) that Shelia is diagnosed as having gestational diabetes?

z = 130 115 / 14 /sqrt 3 = 1.855769

P(x >130) = P(z >1.855769) = 0.9683

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