Question

Binomial distribution:
n=19, p=0.07, q= 0.93 x=2 or more

how do I find the probability of x being 2 or more?

Answer 1

@jdanmath
Do you know the equation for the probability for a particular value of x?

Answer 2

yes but that would mean i have to find for each x value

Answer 3

and then add them up. is there an easier way?

Answer 4

Yes, you can do that, find P(x), x=2,3,4,5,6,7,8,....19.
BUT...

Answer 5

do you know the value of \(\sum_{i=0}^{n} P(i)\)?

Answer 6

no

Answer 7

It means the sum of probabilities for i=0 to i=19 (in this case). Give it some thought?

Answer 8

i see okay

Answer 9

So what is the sum?

Answer 10

190

Answer 11

@jdanmath
Probabilities can never exceed 1, nor less than zero.
In this case, i can only take on values between 0 and 19 (inclusive), so the sum of the probabilities is 1, which means certainty.
Based on that, you can simplify you calculations using the fact:
P(0)+P(1)+.... +P(19)=1
so
P(2)+P(3)+P(4)+....+P(19)=1-(P(0)+P(1))
To solve the problem, you can either do the left-hand side, or the right-hand side, using the formula I gave above for binomial distributions.
Make your choice and finish the calculations! :)

Answer 12

got the right answer this time.. thank you so much!

Answer 13

You're welcome! :)