In pharmacologic research, a variety of clinical chemistry measurements are rout

Question

In pharmacologic research, a variety of clinical chemistry measurements are routinely monitored closely for evidence of side effects of the medication under study. Suppose typical blood-glucose levels are normally distributed, with mean = 90 mg/dL and standard deviation = 38 mg/dL.

A) In some studies only values at least 1.5 times as high as the upper limit of normal are identified as abnormal. What percentage of values would fall in this range?

B) Answer Problem A for values 2.0 times the upper limit of normal.

C) Suppose that in a pharmacologic study involving 6000 patients, 75 patients have blood-glucose levels at least 1.5 times the upper limit of normal on one occasion. What is the probability that this result could be due to chance?

Explanation / Answer

Ans:

Given that

z(65) = (65-90)/38 = -0.6579
z(120) = (120-90)/38 = 0.7895
P(normal range) = P(-0.6579 <= z <= 0.7895)=0.5298

A)1.5*120=180

z(180) = (180-90)/38 = 2.3684

P(x >= 180) = P(z >= 2.3684) = 0.0089

B)

2*120=240

z(240) = (240-90)/38 =3.95

P(x >= 240) = P(z >=3.95) = 0

C)sample proportion=75/6000=0.0125

standard dev=sqrt(0.0089*(1-0.0089)/6000)=0.0012

z=(0.0125-0.0089)/0.0012=3

P(z<3 or z>3)=2*0.00135=0.0027

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