Ge comd glucose level and diabetes are closely related. Let x be a random variable measured 1. in milligrams of glucose per deciliter) 1710 of a liter) of blood. After a 12- hour fast, the random variable x will bave a distribution that is approximately normal with mean µ = 85 and standard deviation ợ = 25 ei2 (s) (Source: Diagnostic Tests with Nursing Implications, edited by S. Loeb, Springhouse Press). Note: After 50 vears of age, both the mean and standard deviation tend to increase. What is the probability that, for an adult (under 50 years old) after 12- hour fast? H=85,0 -25 3edW (d) (a) X is more than 60? bo.85 P(I>60) = Normalcd? CGo, 99999,85,25)-0. &413 %3D (b) X is less than 110? prxx
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
(a) X is more than 60?
bo.85
PrI> 60) = Normalcd C60, 99999,85,25)- 0. 8413
%3D
(b) X is less than 110?
Po
85
110
normal cd? (-1E99, 110, 85,25)
X is between 60 and 110? P C60 <oc< ll0)
= O. 8413
normalcd} C60, 110,85,25)= o.6827
60 85110
(d) X is greater than 140 (borderline diabetes starts at 140)?(P> I40)
normalcd} CiHO,99999,85;25)= 0.0139
(e) Find the 85th percentile.
85 40
Invnormco.85, 85,25)- 10.9108](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F636771b1-1514-4210-adad-8baaefc36388%2F1e299823-3afc-4b8c-aab8-65f1215cc676%2F46nd8cp_processed.jpeg&w=3840&q=75)
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From the provided information,
Mean (µ) = 85
Standard deviation (σ) = 25
X~N (85, 25)
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