Question
Homework7: Problem 9 rk7 m 9 gs (1 point) Shelia's doctor is concemed that she may suffer from gestational diabetes (high blood glucose levels during pregnancy). There is vanation 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 one hour after a sugary drink is ingested. Shelia's measured glucose level one hour after ingesting the sugary dink vanes according to the Normal distribution with mean 129 mg/dl and standard deviation 10 mg/dl. Let L denote a patient's glucose level. ems (a) If measurements are made on three different days, find the level L such that there is probability only 001 that the mean glucose level of three test results falls above L for Shelia s glucose level ANSWER distribution. What is the value of L? (b) If the mean result from the three tests is compared to the crterion 140 mgi'di, what is the probability that Shelia is diagnosed as having gestational diabetes? ANSWER Note:
Explanation / Answer
a)here for 3 test ; std error =std deviation/(n)1/2 =5.7735
for top 0.01 ; z=2.326
hence L =mean +z*std error =142.4312
b)
P(X>140)=1-P(X<140)=1-P(Z<(140-129)/5.7735)=1-P(Z<1.9053)=1-0.9716=0.0284
