# Thread: Probability for binomial distribution

1. ## 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?

2. ## Re: Probability for binomial distribution

Originally Posted by snypeshow
Hey all you binomial distribution fanatics out there!
However the correct answer is 0.844
$\sum\limits_{k = 2}^6 {{\binom{20}{k}{\left( {0.2} \right)}^k}{{\left( {0.8} \right)}^{20 - k}}} = {\text{0}}{\text{.84413219615619}}$
That gives you the given answer.
I suppose they rounded $\sigma=2$.

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

3. ## Re: Probability for binomial distribution

Originally Posted by Plato
$\sum\limits_{k = 2}^6 {{\binom{20}{k}{\left( {0.2} \right)}^k}{{\left( {0.8} \right)}^{20 - k}}} = {\text{0}}{\text{.84413219615619}}$
That gives you the given answer.
I suppose they rounded $\sigma=2$.
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: $\sum\limits_{k = 2}^6$ 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 $\sigma=2$ affect the question, since you aren't using it?

4. ## Re: Probability for binomial distribution

Originally Posted by snypeshow
In this part: $\sum\limits_{k = 2}^6$ 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 $\sigma=2$ affect the question, since you aren't using it?
Go to my edited post. Follow that link. I think that will help.

5. ## Re: Probability for binomial distribution

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