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. 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 drink varies according to the Normal distribution with μ = 135 mg/dL and σ = 12 mg/dL. (Round your answers to four decimal places.)

(a) If a single glucose measurement is made, what is the probability that Shelia is diagnosed as having gestational diabetes?
(b) If measurements are made on four separate days and the mean result is compared with the criterion 150 mg/dL, what is the probability that Shelia is diagnosed as needing further testing for gestational diabetes?

Answer 1

a)
Here, μ = 135, σ = 12 and x = 150. We need to compute P(X >= 150). The corresponding z-value is calculated using Central Limit Theorem

z = (x - μ)/σ
z = (150 - 135)/12 = 1.25

Therefore,
P(X >= 150) = P(z <= (150 - 135)/12)
= P(z >= 1.25)
= 1 - 0.8944 = 0.1056

b)
Here, μ = 135, σ = 12/sqrt(4) = 6 and x = 150. We need to compute P(X >= 150). The corresponding z-value is calculated using Central Limit Theorem

Therefore,
P(X >= 150) = P(z <= (150 - 135)/6)
= P(z >= 2.5)
= 1 - 0.9938
= 0.0062