Glucose in blood A research shows that the distributions of

Glucose in blood. A research shows that the distributions of glucose in human blood levels is unimodel, symmetric, bell-shaped with no apparent outliers. The mean of glycemia is 1.15 mg/ml, and the standard deviation is 0.3 mg/ml. What distribution can we use to model the glycemia levels? What proportion of people will have the glycemia levels higher than 1.5 mg/ml? if we randomly choose 10 people and random variable Y denotes the number of people whose glycemia levels are higher than 1.5 mg/ml. what is the distribution of Y?

Solution

a).

Normal distribution

b).

z=(1.5-1.15)/0.3 = 1.1667

P( x >1.5)= P( z >1.1667)

= 0.1217

c)

Binomial distribution

d).

n=10

p=0.1217

Expectation = np = 1.217

Variance = np(1 - p) = 1.0689

e)

P(X=x) = (_nC_x) p^x (1-p)^n-x  

P(X=0) = (₁₀C₀) 0.1217⁰ (1-0.1217)^10-0  

P( x=0) = 0.2732

f)

P( x 1) = 1-P( x =0)

=1-0.2732

= 0.7268