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 = 86 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

Solution :

(a)

P(x > 60) = 1 - P(x < 60)

= 1 - P[(x - ) / < (60 - 86) / 29]  

= 1 - P(z < -0.90)

= 0.8159

(b)

P(x < 110) = P[(x - ) / < (110 - 86) / 29]

= P(z < 0.83)

= 0.7967

(c)

P(60 < x < 110) = P(x < 110) - P(x < 60) = 0.7967 - 0.1841 = 0.6126

(d)

P(x > 125) = 1 - P(x < 125)

= 1 - P[(x - ) / < (125 - 86) / 29]  

= 1 - P(z < 1.34)

= 0.0901