Sampling distributions

3. Sheila's doctor is concerned that she may suffer from gestational dia- betes (high blood glucose levels during pregnancy). There is a 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 glu- cose level is above 140 milligrams per deciliter one hour after a sugary drink is ingested. Sheila's measured glucose level an hour after ingest- ing a sugary drink varies according to the Normal distribution with M = 125mg/dl and o = 10mg/dl. [2, 10.24] (a) If a single glucose measurement is made, what is the probability that Sheila is diagnosed as having gestational diabetes? (b) If measurements are made on 4 separate days and the mean result is compared with the criterion 140mg/dl, what is the probability that Sheila is diagnosed as having gestational diabetes? (c) Find the level L such that there is a probability of only .05 that the mean glucose level of 4 test results falls above L for Sheila's glucose level distribution. What is the value of L