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

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 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 = 105 mg/dl and = 10 mg/dl. Let X = Sheila's measured glucose level one hour after a sugary drink (a) P(X > 120) = Correct: Your answer is correct. (Use 3 decimal places) Suppose measurements are made on 3 separate days and the mean result is compared with the criterion 120 mg/dl. (b) P(X > 120) = Correct: Your answer is correct. (Use 3 decimal places) (c) What sample mean blood glucose level is higher than 95% of all other sample mean blood glucose levels? Hint: this requires a backward Normal calculation. (Use 2 decimal places)

Explanation / Answer

Ans:

Given that

= 105 mg/dl and = 10 mg/dl.

a)

z=(120-105)/10=1.5

P(z>1.5)=0.0668

There is a 6.68% chance that the glucose level one hour after a surgery drink greater than 120 is, 0.0668.

b)standard error of mean=10/sqrt(3)

z=(120-105)/(10/sqrt(3))

z=2.60

P(z>2.60)=0.0047

c)P(Z<=z)=0.95

z=1.645

Sample mean below which 95% of all other sample mean fall=105+1.645*10/sqrt(3)=114.50

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