Thread: Probability for binomial distribution

Hey all you binomial distribution fanatics out there!

My question is:

Let x be a binomial random variable and suppose n= 20, p=0.2. Then P(μ-σ ≤ x ≤ μ+σ) is:

The following is my attempt:

I know that:
μ = n*p = 20*0.2 = 4
σ = sqrt(npq) = 1.788

So Im looking for the the range of x being between 2.21 and 5.788
But the binomial distribution chart for n = 20 only shows k values for whole numbers, so what I would be looking for is: (k=5)-(k=3), which is 0.804-0.411=0.393

However the correct answer is 0.844

can someone help me solve this?

Originally Posted by snypeshow

Hey all you binomial distribution fanatics out there!
However the correct answer is 0.844

That gives you the given answer.
I suppose they rounded .

On this link scroll down to normal approximations.
That may help with this.

Originally Posted by Plato

That gives you the given answer.
I suppose they rounded .

Thanks so much for helping me with this!

I do have a few questions about what you did (to help further my understanding):

In this part: did you round 2.21 down to 2 and 5.78 up to 6? (just to confirm, this part means the sum of the probabilities when X is between 2 and 6 right?)

or are those numbers totally different? and how would affect the question, since you aren't using it?

Originally Posted by snypeshow

In this part: did you round 2.21 down to 2 and 5.78 up to 6? (just to confirm, this part means the sum of the probabilities when X is between 2 and 6 right?)
or are those numbers totally different? and how would affect the question, since you aren't using it?

Go to my edited post. Follow that link. I think that will help.

ah, ok! That's perfect, thanks so much (again)!!