Posted by Craig on Saturday, June 6, 2009 at 3:13pm.
would this be a binomial-like should i consider it
applicable for study
not applicable for study
Yes, the binomial distribution is a discrete random variable problem.
Basically, if you screen N people, each having a success rate of 0.8. You would like to calculate the minimum candidates to have a minimum of 10 success with a probability of 0.939.
It is a very similar process to flipping coins, except the probability of success is 0.8 instead of 0.5.
The probability can be obtained by tabulation, but the a formula exists to calculate the probability of success of n times out of N candidates, with a probability of success of p.
P(n,N,p)=_{N}C_{n}*p^{N}*(1-p)^{(N-n)}
Let say, since the proability of success is 0.8, and 10 people are required, a good starting point is to screen 10/0.8=13 candidates.
So N=13, p=0.8,
P(10,13,0.8) = 0.246
P(11,13,0.8) = 0.268
P(12,13,0.8) = 0.179
P(13,13,0.8) = 0.055
Probability of retaining 10 or more candidates
= 0.246+0.268+0.179+0.055
= 0.747 < 0.939 required.
So you could screen 14 candidates and calculate the probability. Keep increasing the number of candidates until you get the probability of 0.939 or higher.
Total =
Oh yes, here's a link for more explanation:
http://stattrek.com/Lesson2/Binomial.aspx
Also, in case you are not familiar with the notation,
_{n}C_{r} is the combination function defined as:
_{n}C_{r}
= n!/((n-r)!r!)
=n(n-1)(n-2)...(n-r+1)/r!
For example,
_{13}C_{10}
=13*12*11/(1*2*3)
=286
thank you so much! i think i got it!
what was the answer you finally got