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 milligrams per deciliter (mg/dl) one hour after a sugary drink is ingested. Sheila's measured glucose level one hour after ingesting the sugary drink varies according to the Normal distribution with = 128 mg/dl and = 10 mg/dl. (a) If a single glucose measurement is made, what is the probability that Sheila is diagnosed as havinSheila'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 a sugary drink is ingested. Sheila's measured glucose level one hour after ingesting the sugary drink varies according to the Normal distribution with = 128 mg/dl and = 10 mg/dl.

(a) If a single glucose measurement is made, what is the probability that Sheila is diagnosed as having gestational diabetes? (Round your answer to four decimal places.)


(b) If measurements are made instead on 3 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? (Round your answer to four decimal places.)

g gestational diabetes? (Round your answer to four decimal places.) (b) If measurements are made instead on 3 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? (Round your answer to four decimal places.)

Explanation / Answer

(a) Here mean glucose level one hour after ingesting the sugary drink = 128 mg/dl and standard deviation of glucose level one hour after ingesting the sugary drink = 10 mg/dl.

So,  if the glucose level is above 140 milligrams per deciliter (mg/dl) one hour after a sugary drink is ingested that the  doctor is concerned that she may suffer from gestational diabetes.

Pr(X > 140 ) = NORMAL (X > 140 ; 128 ; 10) = 1 - NORMAL( X < 140; 128 ;10)

Z = (140 - 128)/10 = 1.2

Pr(X > 140 ) = 1 - NORMAL( X < 140; 128 ;10) = 1 - Pr( Z < 1.2) = 1 - 0.8849 = 0.1151

(b) Now observations are taken on 3 sample days and the mean result is compared with the criterion 140 mg/dl.

Standard error of the sample mean = /n = 10/ 3 = 5.7735

Here,

Pr(x > 140) = NORMAL (x > 140; 128 ; 5.7735) = 1 - NORMAL (x < 140; 128 ; 5.7735)

Z = (140 - 128)/ 5.7735 = 2.0785

So,

Pr(x > 140) = 1 - NORMAL (x < 140; 128 ; 5.7735) = 1 - Pr (Z < 2.0785) = 1 - 0.9812 = 0.0188

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