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 μ = 85 and standard deviation σ = 29. 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 125 (borderline diabetes starts at 125)

Answer 1

Given,

= 85 , = 29

We convert this to standard normal as

P(X < x) = P(Z < x - / )

a)

P(X > 60) = P(Z > 60 - 85 / 29)

= P(Z > -0.8621)

= P(Z < 0.8621)

= 0.8057

b)

P(X < 110) = P(Z < 110 - 85 / 29)

= P(Z < 0.8621)

= 0.8057

c)

P(60 < X < 110) = P(X < 110) - P(X < 60)

= P(Z < 110 - 85 / 29) - P(Z < 60 - 85 / 29)

= P(Z < 0.8621) - P(Z < -0.8621)

= 0.8057 - 0.1943

= 0.6114

d)

P(X > 125) = P(Z > 125 - 85 / 29)

= P(Z > 1.3793)

= 0.0839