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 = 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

(d) x is greater than 125 (borderline diabetes starts at 125)

Answer 1

a)

for normal distribution z score =(X-μ)/σ
here mean=       μ=	86
std deviation   =σ=	25.0000

P(  x is more than 60):

probability =

P(X>60)

=

P(Z>-1.04)=

1-P(Z<-1.04)=

1-0.1492=

0.8508

b)

P(  x is less than 110):

probability =	P(X<110)	=	P(Z<0.96)=	0.8315

c)

P( x is greater than 125)

probability =

P(X>125)

=

P(Z>1.56)=

1-P(Z<1.56)=

1-0.9406=

0.0594