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. After a 12-hour fast, the random variable x will have a distribution
that is approximately normal with mean μ=85 and standard deviation σ=25.
After 50 years of age, both the mean and the standard deviation tend to increase.
What is the probability that, for an adult (under 50 years old) after 12-hour
(a) x is more than 60?
(b) x is less than 110?
(c) x is between 60 and 110?
(d) x is greater than 140 (borderline diabetes starts at 140)?
here is how i approach it:
1) the purpose of standard deviation is to be added to or subtracted ([font=lucida sans unicode]±) from the mean value to give you a range of values
2) so, the mathematical application is:
range = 85 [font=lucida sans unicode]± 25
3) determining the range:
upper limit (addition) = 85 + 25 = 110 mg/dl
lower limit (subtraction) = 85 - 25 = 60 mg/dl
so, the range of her blood glucose level is somewhere between 60 mg/dl and 110 mg/dl.
now, normal distribution means a regular bell-curve, which means this calculation satisfies the range of values as well.
you should be able to calculate the rest by using the eqn
shown above for each section of the bell-curve.
here also is a helpful site: http://stattrek.com/lesson2/normal.aspx
Last edit by shaas on Nov 30, '10
What area of stats are you working on right now? Do you guys use tables and z-scores at all? This is how we would approach this problem.. (I think.. lol)
1) First list what is given: (will go with "A" for right now)
μ=85, σ=25, X=60
2) List what you're looking for: Find the probability that X >60
3) Find Z: [FONT=Geneva]z= x-μ/σ
Z= 60-85/25= -1
4) Convert Z to a percent (Using using statistic table A or B- can't remember exactly)
-1 = 34.13%
5) Convert percent to a probability. (Simply move the decimal)
6) Fine probability: To find a probability at or above- subtract from .5 to find a probability at or below we add to .5
.5- .3413 = .1587 (for "b" you'll add the probability to .5)
6) List answer:
There is a .1587 probably that X is above 60..
I might be totally off base.. this is based on our chapter in statistics and parameters.
Last edit by lifelearningrn on Nov 30, '10