# Binomial Distribution : Probability equation solution

##### New Member
Question :In a binomial distribution for p=.48, q=1-p=.52 find the population size n1 so that P(X>=3)=.95

My solution :
P(X>=3)=.95
can be rewrite as
P(X=0)+P(X=1)+P(X=2)=.05 ------------------------------------------ eq(1)
but i am un able to solve the above equation for n1,

Is there any way to solve the equation (1) or is there any alternate solution?

#### Buckeye

##### Active Member
Your equation is correct, but you need to "plug in" the probabilities for X=0, X=1, and X=2. You need to use this: $$\sum_{x = 0}^n {n \choose{x}} p^x (1-p)^{n-x}$$

Assuming you did this, I understand your frustration. The equation is a little messy. Still pondering it.

Last edited:

#### rogojel

##### TS Contributor
hi,
trial and error? There are only a few possible choices for n.
regards