Sheila\'s doctor is concerned that she may suffer from gestational diabetes (hig

Question

Sheila'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 miligrams per deciliter (mg/dl) one hour after having a sugary drink. Sheila's measured glucose level one hour after the sugary drink varies according to the Normal distribution with = 125 mg/dl and = 15 mg/dl.

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

Explanation / Answer

a) z-score = (140-125)/10.
Now, looking up the p-value as we want to find the probability that Shelia's glucose level exceeds 140.
So, our answer will be 1 - looked up p-value.

b) z-score = (140-125)/(10/sqrt(6)).
Again use the same procedure as in 1.
Here, note that the standard deviation from the mean dropped significantly due to the average over a larger number of samples in this test.
Thus, the probability that she is diagnosed is lower (which is the true result since her mean glucose level is 125 way below 140).

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