Interpreting Binomial CDF results I have a Binomial distribution CDF, and was trying to interpret the results. For this, I have $n=100$ trials, with $p=0.25$. When computing the CDF, I have:
$P(X \leq 25) = 0.5535$
Does this mean that the probability of obtaining $\leq$ 25 successes in 100 trials is 55.35%. Further, if I was to compute:
$1 - P(X \leq 25)  = 0.446$,
Does this mean that the probability of obtaining more than 25 successes in 100 trials is 44.6%?
Thanks.

If $X \sim \mathsf{Binom}(n=100, p=.25),$ then you say $$P(X > 25) =
1 - P(X \le 25) = 0.4465,$$ to four places. This is the probability
that some one of the values 26 through 100 will occur. In particular,
one of these values is 90; its share of that overall probability is
$P(X = 90) \approx 0$ (positive but very tiny). [Using R, were a binomial PDF is dbinom and CDF is pbinom.]
1 - pbinom(25, 100, .25)
[1] 0.4465292
dbinom(90, 100, .25)
[1] 6.360895e-43

It may help your intuition to recall that $X$ is approximately normal
with $\mu = E(X) = np = 25$ and $\sigma = SD(X) = \sqrt{np(1-p)} =  4.3301.$

R code for figure.
x = 0:100;  PDF = dbinom(x, 100, 0.25)
hdr = "PDF of BINOM(100, .25) [blue bars] with Approximating Normal Density"
plot(x, PDF,  type="h", col="blue", lwd=2, main=hdr)
 curve(dnorm(x, 25, 4.3301), add=T, col="maroon", lwd=2)
 abline(h=0, col="green2");  abline(v=0, col="green2")

