How to find the number of trials for a binomial distribution using a GDC?

Question

I am given a discreet random variable X that satisfies the binomial distribution with p = 0.5 and number of trials 2n. I also know that P(X=n) is 0.273. I have to find the value of n and I am expected to use a GDC (mine is Casio fx-cg50). How do I proceed?

Thanks in advance!

Answer 1

By simple inspection you easy find that $n=4$, no Graphic Display Calculator is needed

• $n=0;1$ obviously incorrect, no calculations are needed

• $n=2$, incorrect as

$P(n=2)=6\cdot 0.5^4=0.375$

• $n=3$, incorrect as

$P(n=3)=20\cdot 0.5^6=0.313$

• $n=4$, correct, as

$P(n=4)=70\cdot 0.5^8=0.273$