# Math Help - Binomial distribution

1. ## 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?

2. ## Re: Binomial distribution

Why not upload the image here?

3. ## 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)?

4. ## Re: Binomial distribution

$P[X\leq 65|100,0.7]=0.16286$

5. ## Re: Binomial distribution

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.

6. ## Re: Binomial distribution

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

How did you calculate this?

8. ## 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.

9. ## Re: Binomial distribution

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.

10. ## 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.

11. ## Re: Binomial distribution

Yes it should have been 65.5.