# Binomial distribution

• Sep 14th 2012, 12:14 PM
KarlssonKK
Binomial distribution
I have an assignment image.png - Speedy Share - upload your files here which is a bit different,
I have to use Mathematics Handbook for Sience and Engineering to solve the problem,
I can look it up in tables. But the tables for binomial functions is only up to 20,
Normal Distribution to 3.4 and Poisson up to 24 in some cases.
So how do I do it? Approximation of some kind?
• Sep 14th 2012, 01:32 PM
a tutor
Re: Binomial distribution
Why not upload the image here?
• Sep 14th 2012, 10:21 PM
chiro
Re: Binomial distribution
Hey KarlssonKK.

The asymptotic distribution results are such that (X - E[X])/SQRT(Var(X)) ~ N(0,1).

So to start off, can you calculate the mean and the variance of your distribution? Using this result, can you then construct a corrected interval (remember that for a binomial, you should find a probability corresponding to 64.5 and not 64 because of the disjoint nature of the binomial)?
• Sep 14th 2012, 11:22 PM
MaxJasper
Re: Binomial distribution
$P[X\leq 65|100,0.7]=0.16286$

http://mathhelpforum.com/attachment....1&d=1347690649
• Sep 15th 2012, 10:31 AM
KarlssonKK
Re: Binomial distribution
Quote:

Originally Posted by chiro
Hey KarlssonKK.

The asymptotic distribution results are such that (X - E[X])/SQRT(Var(X)) ~ N(0,1).

So to start off, can you calculate the mean and the variance of your distribution? Using this result, can you then construct a corrected interval (remember that for a binomial, you should find a probability corresponding to 64.5 and not 64 because of the disjoint nature of the binomial)?

Yes I can calculate the variance but I'm note sure thats the way to go, but if I do, what do I do then?
and what do you mean by finding a propability corresponding to 64,5? I understand that I should not include 65 since it is
<60 and not =<60.
• Sep 15th 2012, 10:32 AM
KarlssonKK
Re: Binomial distribution
Quote:

Originally Posted by MaxJasper
$P[X\leq 65|100,0.7]=0.16286$

http://mathhelpforum.com/attachment....1&d=1347690649

How did you calculate this?
• Sep 15th 2012, 10:40 AM
MaxJasper
Re: Binomial distribution
• Sep 15th 2012, 12:41 PM
HallsofIvy
Re: Binomial distribution
The reason you should calculate the standard deviation (and mean) is that a binomial distribution with large number of 'trials' can be approximated by the normal distribution with the same mean and standard deviation.
• Sep 15th 2012, 01:17 PM
a tutor
Re: Binomial distribution
Quote:

Originally Posted by chiro
you should find a probability corresponding to 64.5 and not 64 because of the disjoint nature of the binomial)?

I think that should be 65.5.

Using the binomial calculation above we get about 0.1629.

Using the normal approximation we get about 0.1631.
• Sep 15th 2012, 03:19 PM
HallsofIvy
Re: Binomial distribution
If the problem is to find the probability that the number of "successes" is 64, then you should use the normal approximation to find the probability that x is between 64.5 and 65.5.
• Sep 15th 2012, 06:04 PM
chiro
Re: Binomial distribution
Yes it should have been 65.5.