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 = 89 and standard deviation σ = 22.

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

mean= u = 89

standard deviation = s = 22

a) P ( X > 60 )

Z-score = ( X - u)/s

Z(60) = ( 60 - 89) /22 = -1.3181

P( Z > -1.3181 ) = 0.9063

b) P( X < 110 )

Z (110 ) = (110 -89)/22

P ( Z < 0.9545 ) = 0.8301

(c) Between 60 and 110

Z(60) = -1.3181

Z(110) = 0.8301

P( -1.3181 < Z < 0.8301 ) = 0.7363

(d)

P ( X > 125 )

Z(125) = (125- 89)/22

P( Z >  1.6363 ) =0.0509