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Diabetes Equipment

September 2nd, 2010 admin

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Stats Help Probability?

It’s believed that 4% of children have a gene that may be linked to juvenile diabetes. Researchers at a firm would like to test new monitoring equipment for diabetes. Hoping to have 20 children with the gene for their study, the researchers test 732 randomly selected newborns for the presence of the gene linked to diabetes. What’s the probability that they find enough subjects for their study?

Copy and paste into excell:
=BINOMDIST(20,732,0.04,TRUE)
=0.043033722
=4.3%

What it means is if you have a perfectly normal distribution (bell curve), it gives you the probability of fulfilling it. 20 is the trial you are on, 732 is the total number of trials, .04 is the overall probability of any given trial, True is cumulative, False if non cumulative (ie the probability of getting it in that trial, cumulative is for all trials up until that one).

Try:
=BINOMDIST(40,732,0.04,TRUE)
=97.9%

Basicaly in 40trials you are pretty much guaranteed to to find the proper number, but at 20 trials you are only at 4.3%

BTW Kyle did the same thing except he did not do cumulative. All you have to do, is sum each instance 1-20 using Kyle’s method.

Kyle posted the following (he deleted his answer for some reason), btw, props Kyle excellent work showing:
Use the binomial theorem.

for x successes in n trials:

Combination(of n objects taken r at a time) * p^x * q^(n-x)

-or-

n! / [ (n-x)! * x! ] * p^x * q^(n-x)

We know our values here:
p = probability of “success” = 4% = 0.04
q = probability of “failure” = 1 – p = .96
x = desired number of success = 20
n = total number of trials = 732

Substituting our “knowns” into the binomial theorem:
n! / [ (n-x)! * x! ] * p^x * q^(n-x)
= 732! / [ (732 - 20)! * 20! ] * 0.04^20 * 0.96^(732 – 20)
= 0.0161686 = approximately 1.62%


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