A person\'s blood glucose level and diabetes are closely related. Let x be a ran

Question

A person's blood glucose level and diabetes are closely related. Let x be a random variable measured in milligrams of glucose per deciliter (1/10 of a liter) of blood. Suppose that after a 12-hour fast, the random variable x will have a distribution that is approximately normal with mean = 89 and standard deviation = 25. Note: After 50 years of age, both the mean and standard deviation tend to increase. For an adult (under 50) after a 12-hour fast, find the following probabilities. (Round your answers to four decimal places.)

(a) x is more than 60

(b) x is less than 110


(c) x is between 60 and 110


(d) x is greater than 140 (borderline diabetes starts at 140)

Explanation / Answer

Sigma = 25

Mean = 89

P(X>60) = P(Z>60-89/25) = P(Z>-1.16) = 1-.1230 = .8770

P(X<110)= P(Z<110-89/25) = P(Z< .84) = .7995

P(60<X<110) = .8770-.7995 = .8770-.7995 = .0775

P(X>140) = P( Z> 140=89/25)= P(Z> 2.04) = 1-.9791 = .0209

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