Binomial Distribution Calculator
Calculate probabilities of the binomial distribution step by step
The calculator will find the simple and cumulative probabilities, as well as the mean, variance, and standard deviation of the binomial distribution.
Your Input
Calculate the various values for the binomial distribution with $$$n = 20$$$, $$$p = 0.3 = \frac{3}{10}$$$, and $$$x = 5$$$.
Answer
Mean: $$$\mu = n p = \left(20\right)\cdot \left(\frac{3}{10}\right) = 6$$$A.
Variance: $$$\sigma^{2} = n p \left(1 - p\right) = \left(20\right)\cdot \left(\frac{3}{10}\right)\cdot \left(1 - \frac{3}{10}\right) = \frac{21}{5} = 4.2$$$A.
Standard deviation: $$$\sigma = \sqrt{n p \left(1 - p\right)} = \sqrt{\left(20\right)\cdot \left(\frac{3}{10}\right)\cdot \left(1 - \frac{3}{10}\right)} = \frac{\sqrt{105}}{5}\approx 2.04939015319192.$$$A
$$$P{\left(X = 5 \right)}\approx 0.17886305056988$$$A
$$$P{\left(X \lt 5 \right)}\approx 0.237507778877602$$$A
$$$P{\left(X \leq 5 \right)}\approx 0.416370829447481$$$A
$$$P{\left(X \gt 5 \right)}\approx 0.583629170552519$$$A
$$$P{\left(X \geq 5 \right)}\approx 0.762492221122398$$$A