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 = 26. 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, mean=4=86 Standard deviation=o=26 a>x is more than 60 Answer: PlX7G /x-M - 60-86 26 =P(Z >-10) = 1- Plz<-1,0) using z-table, we get = 1-0.1587 Plx>60) = 0.8413

110 by x is less than Answer: Plx<110) olx-M 120-86 26 = P (Z <0.92) using 2-table, we get P(x<110) = 0.82127

YX is between Go and llo Answer: TP160<xsllo 160-86, X-M, 110-861 26 r .:26 = P(-1.05 2 < 0.92) =P(Z <0.92)-P(25-10) using z-table, we get = .0.8212 -0.1587 P (60sx4110) = 0.66251

7 X is greater than 125 Answer: P(x >125) - 125-86 26 = P(271.50) = 1- P1 2<1.50) using 2-table, we get o 1-0.9332 P(x>125) = 0.0668/