Question

1. A patient is classified as having gestational diabetes if their average glucose level is above 140 milligrams per deciliter (mg/dl) one hour after a sugary drink is ingested. Rebecca's doctor is concerned that she may suffer from gestational diabetes. There is variation both in the actual glucose level and in the blood test that measures the level. Rebecca's measured glucose level one hour after ingesting the sugary drink varies according to the Normal distribution with μ= 140+# mg/dl and σ = #+1 mg/dl, where # is the last digit of your GCU student ID number. Using the Central Limit Theorem, determine the probability of Rebecca being diagnosed with gestational diabetes if her glucose level is measured:

1. Once?
2. #+2 times, where # is the last digit of your student ID?
3. #+4 times, where # is the last digit of your student ID?

Comment on the relationship between the probabilities observed in (a), (b), and (c). Explain, using concepts from lecture why this occurs and what it means in context

Answer 1

- - A patient is elabritied having gestational diabetes of their is average glucose level obove 140 milligrams The Rebecca'ls dectors is concerned that she may subtering from gestational diabetes. . Rebecca's measurived glucose level one hour offer ingesting the Sugar drink varies - Normal distribution M = 141 mg lat o 2 nglale Average glucose level = 140 milligrams 140-M a 140-141 z= -05 .. from z-table -> p (72-0.5) = 06915

Z = 140-M 140-14! 2 162) 2/114142 1704142 (. 1.4142 from Z - Table) Z = -0.7071 >> P Z>-017071) = 0.7794 Z = 140.M 140-141 214 - 212 = -1 From Z-table] Zz - 1.0 P (Z2-1.0] = 0.3413