13.32 (EX) Glucose testing 1/3: Shelia’s doctor is concerned that she may suffer

Question

13.32 (EX) Glucose testing 1/3: 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 her glucose level is above 140 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 = 125 mg/dl and = 10 mg/dl.

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

P(X > 140) = P(Z > [1]) = [2]. (Round the 1st number to 1 decimal and the 2nd number to 4 decimals)

Glucose testing 2/3: 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?

Explanation / Answer

a) Let be X: The patients classified as having gestational diabetes if the glucose level is above 140 milligrams per deciliter (mg/dl) one hour after a sugary drink

X n(125 ; 10)

P(X > 140) = P((X - 125)/10 > (140 - 125)/10) = P(Z > 1.5) = 0.0668

b) n = 4
x1, x2, x3, x4

Xmean = (x1 + x2+x3 + x4)/4

By LCT

Xmean n(125 ; 10/sqrt(4))

Xmean n(125 ; 5)

P(Xmean > 140) = P((Xmean - 125)/5 > (140 - 125)/5) = P(Z > 3) = 0.0014

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