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Normal Distribution and Probability of Glucose Level

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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. A patient is classified as having gestational diabetes if the glucose level is above 140 milligrams per deciliter (mg/dl) one hour after having a sugary drink. Shelia's measured glucose level on hour after the sugary drink varies according to the Normal distribution with the mean (the Greek letter mu-mean of a population) =125 mg/dl and the standard deviation =10 mg/dl.

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 4 separate days and the mean result is compared with the criterion 140 mg/dl, what is the probability that Shelia is diagnosed as having gestational diabetes?

Glucose testing, continued. Shelia's measured glucose level one hour after a sugary drink varies according to the Normal distribution with the mean = 125 mg/dl and standard deviation = 10mg/dl. What is the level L such that there is probability only 0.05 that the mean glucose level of 4 test results falls above L? (Hint: This requires a backward Normal calculation.)

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a) Mean = 125mg/dl
Standard Deviation =10mg/dl
Sample Size, n = 1
z-score = {(140-125)/10 ...

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