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 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 9 mg/dl. Let LL denote a patient's glucose level.

(a) If measurements are made on four different days, find the
level LL such that there is probability only 0.05 that the mean
glucose level of four test results falls above LL for Shelia's
glucose level distribution. What is the value of LL?

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

Answer #1

Given,

= 127, = 9

The central limit theorem is

P( < x) = P( Z < x - / ( / sqrt(n) )

a)

We have to calculate L such that P( > L) = 0.05

Therefore,

P( > L) = 0.05

P( Z > L - / ( / sqrt(n) ) = 0.05

P( Z < L - / ( / sqrt(n) ) = 0.95

From the Z table, z-score for the probability of 0.95 is 1.645

Therefore,

L - / ( / sqrt(n) = 1.645

Put the value of , and n in above expression and solve for L.

L - 127 / (9 / sqrt(4 ) ) = 1.645

L - 127 = 1.645 * (9 / sqrt(4 ) )

= 134.4025

**Value of L = 134.40**

b)

Using central limit theorem,

P( < x) = P( Z < x - / ( / sqrt(n) )

P( < 140) = P( Z < 140 - 127 / (9 / sqrt(4) ) )

= P( Z < 2.89)

= **0.9981**

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...

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. In a test to screen for
gestational diabetes, a patient is classified as needing further
testing for gestational diabetes if the glucose level is above 150
milligrams per deciliter (mg/dL) one hour after a sugary drink.
Shelia's measured glucose level one hour after the sugary...

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. In a test to screen for
gestational diabetes, a patient is classified as needing further
testing for gestational diabetes if the glucose level is above 145
milligrams per deciliter (mg/dL) one hour after a sugary drink.
Shelia's measured glucose level one hour after the sugary...

Sheila'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 is
ingested. Sheila's measured glucose level one hour after ingesting
the sugary drink varies according to the Normal distribution with...

Sheila'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 is
ingested. Sheila's measured glucose level one hour after ingesting
the sugary drink varies according to the Normal distribution with...

Sheila'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
miligrams per deciliter (mg/dl) one hour after having a sugary
drink. Sheila's measured glucose level one hour after the sugary
drink varies according to the Normal distribution with μμ =...

(1 point) Sheila'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
miligrams per deciliter (mg/dl) one hour after having a sugary
drink. Sheila's measured glucose level one hour after the sugary
drink varies according to the Normal distribution with...

Sheila'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 her glucose level is above 120
milligrams per deciliter (mg/dl) one hour after a sugary drink.
Sheila's measured glucose level one hour after the sugary drink
varies according to the Normal distribution with μ = 105...

Sheila'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
miligrams per deciliter (mg/dl) one hour after having a sugary
drink. Sheila's measured glucose level one hour after the sugary
drink varies according to the Normal distribution with μμ =...

4.
Suppose an expectant mother’s doctor is concerned that the patient
may suffer from gestational diabetes (high blood glucose levels
during pregnancy). A patient is considered to
have gestational diabetes if her glucose level is above 140
milligrams per deciliter (mg/dl) one hour after the intake of a
sugary drink. Assume the patient’s measured glucose level one hour
after taking a sugary drink is distributed normally with μ = 125
mg/dl and σ = 10 mg/dl.
(a) If
a single...

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 18 minutes ago

asked 18 minutes ago

asked 20 minutes ago

asked 26 minutes ago

asked 33 minutes ago

asked 38 minutes ago

asked 54 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago