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 the glucose level is above140milligrams per deciliter one hour after a sugary drink is ingested. Shelia's measured glucose level one hour after ingesting the sugary drink varies according to the Normal distribution with mean127mg/dl and standard deviation8mg/dl. LetLdenote a patient's glucose level.

(a) If measurements are made on four different days, determineLsuch that there is a probability of only0.04 that the mean glucose level of four test results falls aboveL for Shelia's glucose level distribution. What is the value ofL? In other words, determine the value ofL so thatP(x>L)=0.04

Answer:

(b) If measurements are made on four different days, and the mean result from the four tests is compared to the criterion140 mg/dl, what is the probability that Shelia is diagnosed as having gestational diabetes?

Answer: