Sheila\'s doctor is concerned that she may suffer from gestational diabetes (hig
ID: 3125571 • Letter: S
Question
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 = 129 mg/dl and = 10 mg/dl. (a) If a single glucose measurement is made, what is the probability that Sheila is diagnosed as having gestational diabetes? (Round your answer to four decimal places.) (b) If measurements are made instead on 2 separate days and the mean result is compared with the criterion 140 mg/dl, what is the probability that Sheila is diagnosed as having gestational diabetes? (Round your answer to four decimal places.)
Explanation / Answer
a)
We first get the z score for the critical value. As z = (x - u) / s, then as
x = critical value = 140
u = mean = 129
s = standard deviation = 10
Thus,
z = (x - u) / s = 1.1
Thus, using a table/technology, the right tailed area of this is
P(z > 1.1 ) = 0.135666061 [ANSWER]
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b)
We first get the z score for the critical value. As z = (x - u) sqrt(n) / s, then as
x = critical value = 140
u = mean = 129
n = sample size = 2
s = standard deviation = 10
Thus,
z = (x - u) * sqrt(n) / s = 1.555634919
Thus, using a table/technology, the right tailed area of this is
P(z > 1.555634919 ) = 0.059897465 [ANSWER]
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