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

last number of id is 8

Answer 1

the Central limit theorem states that if you have a populationiwth mean mu and Standard Deviation sigma and it takes suffiencently large ransom smaples from the population with replacement then the istribution of the sample means will be approximately normally distributed.

Here in this question if the doctor is taking only one sample of Rebecca's glucose level , there can be too much variability and the assumption can be wrong so the doctor should go for more number of trials to arrive into a correct conclusion.Increasing the sample size reduces the sampling error.

In the question if we apply value to # as 8 from the Z table we get values for (a) as 0.18943 (b) as 0.00248 (c) as0.00107 the relation is obvious that when the n is becoming larger the probability of Rebecca's glucose level above 140 is coming down so the doctor can take a decision on the basis of the above values. if from only on test the doctor would have taken a decision then he would consider a chance of 18% while when the number of trials increased it has come doen to 1%.

The calculation of Z values are as follows