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, Using the Central Limit Theorem, determine the probability of Rebecca being diagnosed with gestational diabetes if her glucose level is measured:
   1. Once?
   2. n=2 times,
   3. n=4 times,
   4. 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.

For each part, insert your sketch of the required area under the normal curve. In addition, include a screenshot of your Excel computation to find this area.

1. Insert screenshot and figure for part (a)

2. Insert screenshot and figure for part (b)

3. Insert screenshot and figure for part (c)

4. Comment on the relationship among the probabilities in parts (a),(b), and (c).

Answer 1

(a) The Excel output is:

The formulas are:

The curve is:

(b) The Excel output is:

The formulas are:

The curve is:

(c) The Excel output is:

The formulas are:

The curve is:

(d) The answers are the same because the X and μ values are the same which makes the upper term 0.