試行回数 $$$n = 100$$$、成功確率 $$$p = 0.2$$$ の二項分布に従う $$$P{\left(X = 20 \right)}$$$ を求めよ

$$$n = 100$$$、$$$p = 0.2 = \frac{1}{5}$$$、$$$x = 20$$$を用いて二項分布のさまざまな値を計算します。

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

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

標準偏差: $$$\sigma = \sqrt{n p \left(1 - p\right)} = \sqrt{\left(100\right)\cdot \left(\frac{1}{5}\right)\cdot \left(1 - \frac{1}{5}\right)} = 4$$$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