Shelia\'s doctor is concerned that she may suffer from gestational diabetes (hig

Question

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 above 140 milligrams per deciliter (mg/dl) one hour after a sugary drink. Shelia's measured glucose level one hour after the sugary drink varies according to the Normal distribution with ? = 122 mg/dl and ? = 12 mg/dl. If a single glucose measurement is made, what is the probability that Shelia is diagnosed as having gestational diabetes? Give your answer to 4 decimal places. If measurements are made on 5 separate days and the mean result is compared with the criterion 140 mg/dl, what is the probability that Shelia is diagnosed as having gestational diabetes? Give your answer to 4 decimal places.

Explanation / Answer

We are given that 4 glucose measurements are made so we are working with the sampling distribution which is Normal with a mean = 125 mg/dl and = 10/sqrt(4) = 5 mg/dl.

We want to know the probability that the mean result is greater than 140.

Calculator Method We will use the normalcdf function in the calculator with a lower bound of 140 and an upper bound of 1E99, the crazy mathematicians way.

Normalcdf (140, 1E99,125,5) = 0.0013 Thus the probability is 1.3% Table Method We will need a z-score for 140. We get z = (140- 125) /5=3 which has a table value of 0..9987

To get the area we want we must subtract the number from 1, 1-0.9987 = 0.0013 .

The probability is 1.3%.

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