Question

what is the binomial probability of the following:
P(X < 5)
P(X less than or equal to 10)
P(4 < X greater than or equal to 9)

Answer 1

Do you mean in a coin experiment? I think the probabily of success must be given.

Answer 2

Oh yea im sorry. n=12 p=.3 so q=.7

Answer 3

Apply the binomial distribution function,
\[P(X<5)=\sum_{k=1}^{4}\binom {12}k p^kq^{12-k}\] For the second part,
\[P(X\leq 10)=1-\sum_{k=1}^{2}\binom {12}kp^kq^{n-k}\] For the third part
\[P(X\geq 4)=1-\sum_{k=1}^{3}\binom {12}kp^kq^{n-k}\]

Answer 4

Sorry, the sums must be from k=0.

Answer 5

Results,
0.723655
0.747185
0.507484

Answer 6

the second two arent right

Answer 7

True, it must be, for the second 0.999985, and the third it must be, this one,
\[P(4<X\leq 9)=P(X=5)+P(X=6)+P(X=7)+P(X=8)+P(X=9)=0.276138\]