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 = 126 mg/dl and = 10 mg/dl. What is the level L such that there is probability only 0.05 that the mean glucose level of 2 test results falls above L for Sheila's glucose level distribution? (Round your answer to one decimal place.)

Explanation / Answer

NORMAL DISTRIBUTION
the PDF of normal distribution is = 1/ * 2 * e ^ -(x-u)^2/ 2^2
standard normal distribution is a normal distribution with a,
mean of 0,
standard deviation of 1
equation of the normal curve is ( Z )= x - u / sd ~ N(0,1)
mean ( u ) = 126
standard Deviation ( sd )= 10
P ( Z > x ) = 0.05
Value of z to the cumulative probability of 0.05 from normal table is 1.6449
P( x-u / (s.d) > x - 126/10) = 0.05
That is, ( x - 126/10) = 1.6449
--> x = 1.6449 * 10+126 = 142.4485 ~ 142.4

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