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 μ = 128 mg/dl and σ = 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 3 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.)

Answer 1

Let X be the pulse rate of women X ~ N(71.4, 11.8^2) then Z = X - 71.4/11.8 ~ N(0, 1), a standard normal variate For P_1 , Z = -2.33, For P_99, Z = 2.33 implies X - 7.4/11.8 = -2.33 implies X = 98.894 implies X = 43.906 therefore P_99 = 98.9 beats/min therefore P_1 = 43.9 beats/min Let x^bar be the mean of 30 women P(58 < X^bar < 84) = P(58 - 71.4/11.8 < Z < 84 - 71.4/11.8) = P(-1.14 < Z < 1.07) = 0.7306 The prob is 0.7306 Answer is (B) (a) is based on population parameter So cutoff values should be based on (a).

Answer 2

The answer shown does not correspond to the question