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 one hour after a sugary drink is ingested. Shelia's measured glucose level one hour after ingesting the sugary drink varies according to the Normal distribution with mean 127 mg/dl and standard deviation 10 mg/dl. Let L denote a patient's glucose level. ### Problem Statement:**(a)** If measurements are made on three different days, find the level \( L \) such that there is a probability of only 0.02 that the mean glucose level of three test results falls above \( L \) for Sheila's glucose level distribution. - **Answer:** 133.2**(b)** If the mean result from the three tests is compared to the criterion of 140 mg/dl, what is the probability that Sheila is diagnosed as having gestational diabetes?- **Answer:** 0.1587### Explanation:The problem provides a statistical analysis of glucose levels measured over three different days. - **(a)** Involves finding a critical value \( L \) where there is a very low probability (2%) that the average glucose level exceeds \( L \). - **(b)** Calculates the probability that the average glucose level is above a specific criterion (140 mg/dl), which would indicate gestational diabetes.These problems often involve understanding normal distribution and utilizing statistical tables or software to determine probabilities and critical values.

Answered: Shelia's doctor is concerned that she…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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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 one hour after a sugary drink is ingested. Shelia's measured glucose level one hour after ingesting the sugary drink varies according to the Normal distribution with mean 127 mg/dl and standard deviation 10 mg/dl. Let L denote a patient's glucose level.

### Problem Statement:

**(a)** If measurements are made on three different days, find the level \( L \) such that there is a probability of only 0.02 that the mean glucose level of three test results falls above \( L \) for Sheila's glucose level distribution.

- **Answer:** 133.2

**(b)** If the mean result from the three tests is compared to the criterion of 140 mg/dl, what is the probability that Sheila is diagnosed as having gestational diabetes?

- **Answer:** 0.1587

### Explanation:

The problem provides a statistical analysis of glucose levels measured over three different days.

- **(a)** Involves finding a critical value \( L \) where there is a very low probability (2%) that the average glucose level exceeds \( L \).

- **(b)** Calculates the probability that the average glucose level is above a specific criterion (140 mg/dl), which would indicate gestational diabetes.

These problems often involve understanding normal distribution and utilizing statistical tables or software to determine probabilities and critical values.

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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