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Find $$$P{\left(X = 20 \right)}$$$ for binomial distribution with $$$n = 100$$$ and $$$p = 0.2$$$

The calculator will find the probability that $$$X = 20$$$ for the binomial distribution with $$$n = 100$$$ and $$$p = 0.2$$$.

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Your Input

Calculate the various values for the binomial distribution with $$$n = 100$$$, $$$p = 0.2 = \frac{1}{5}$$$, and $$$x = 20$$$.

Answer

Mean: $$$\mu = n p = \left(100\right)\cdot \left(\frac{1}{5}\right) = 20$$$A.

Variance: $$$\sigma^{2} = n p \left(1 - p\right) = \left(100\right)\cdot \left(\frac{1}{5}\right)\cdot \left(1 - \frac{1}{5}\right) = 16$$$A.

Standard deviation: $$$\sigma = \sqrt{n p \left(1 - p\right)} = \sqrt{\left(100\right)\cdot \left(\frac{1}{5}\right)\cdot \left(1 - \frac{1}{5}\right)} = 4$$$A.

$$$P{\left(X = 20 \right)}\approx 0.099300214808825$$$A

$$$P{\left(X \lt 20 \right)}\approx 0.460161370064573$$$A

$$$P{\left(X \leq 20 \right)}\approx 0.559461584873398$$$A

$$$P{\left(X \gt 20 \right)}\approx 0.440538415126602$$$A

$$$P{\left(X \geq 20 \right)}\approx 0.539838629935427$$$A