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 µ = 134 mg/dl and s = 13 mg/dl.

a. If a single glucose measurement is made, what is the probability (±0.0001) that Shelia is diagnosed as having gestational diabetes?   

b. If measurements are made on 543276 separate days and the mean result is compared with the criterion 140 mg/dl, what is the probability (±0.0001) that Shelia is diagnosed as having gestational diabetes?

Explanation / Answer

Solution:

We are given

Glucose level follows normal distribution.

Mean = 134

SD = 13

Part a

We have to find P(X>140)

P(X>140) = 1 – P(X<140)

Z = (X – Mean) / SD

Z = (140 – 134) / 13

Z = 6/13

Z = 0.461538

P(Z< 0.461538) = P(X<140) = 0.677794

P(X>140) = 1 – P(X<140)

P(X>140) = 1 – 0.677794

P(X>140) = 0.322206

Required probability = 0.322206

Part b

We are given n = 543276

µ = Population Mean = 134

= Population SD = 13

P(Xbar>140) = 1 – P(Xbar<140)

Z = (Xbar - µ) / [/sqrt(n)]

Z = (140 – 134) / [13/sqrt(543276)]

Z = 6/[13/sqrt(543276)]

Z = 340.1873

P(Z<340.1873) = P(Xbar<140) = 1.0000

P(Xbar>140) = 1 – P(Xbar<140)

P(Xbar>140) = 1 – 1

P(Xbar>140) = 0.0000

Required probability = 0.0000

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