Question

Fasting blood glucose (FBG) levels can be used to diagnose whether someone has Type 2 diabetes. Among non-diabetic individuals, FBG levels are approximately normally distributed with mean 100 mg/dL and standard deviation 12 mg/dL.

i. What FBG level is needed to be in the upper 1% of the distribution for non-diabetic individuals?

ii. An individual is classified as pre-diabetic if two consecutive FBG measurements are between 100 and 125 mg/dL. Calculate the probability of a non-diabetic being classi- fied as pre-diabetic, under the assumption that these two consecutive measurements are independent.

Answer 1

Solution :

Given that,  

mean = = 100

standard deviation = = 12

i.

Using standard normal table ,

P(Z > z) = 1%

1 - P(Z < z) = 0.01

P(Z < z) = 1 - 0.01

P(Z < 2.33) = 0.99

z = 2.33

Using z-score formula,

x = z * +

x = 2.33 * 12 + 100 = 127.96

FBG leve = 127.96

ii.

P(100 < x < 125) = P[(100 - 100)/ 12) < (x - ) /  < (125 - 100) / 12) ]

= P(0 < z < 2.08)

= P(z < 2.08) - P(z < 0)

= 0.9812 - 0.5

= 0.4812

Probability = 0.4812