Binomial Distribution : Probability equation solution

#1
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?
 
#2
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.
 
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