Trova $$$P{\left(X = 1 \right)}$$$ per la distribuzione binomiale con $$$n = 8$$$ e $$$p = 0.12$$$

Calcola i vari valori per la distribuzione binomiale con $$$n = 8$$$, $$$p = 0.12 = \frac{3}{25}$$$ e $$$x = 1$$$.

Media: $$$\mu = n p = \left(8\right)\cdot \left(\frac{3}{25}\right) = \frac{24}{25} = 0.96$$$A.

Varianza: $$$\sigma^{2} = n p \left(1 - p\right) = \left(8\right)\cdot \left(\frac{3}{25}\right)\cdot \left(1 - \frac{3}{25}\right) = \frac{528}{625} = 0.8448$$$A.

Deviazione standard: $$$\sigma = \sqrt{n p \left(1 - p\right)} = \sqrt{\left(8\right)\cdot \left(\frac{3}{25}\right)\cdot \left(1 - \frac{3}{25}\right)} = \frac{4 \sqrt{33}}{25}\approx 0.919130023446085.$$$A

$$$P{\left(X = 1 \right)}\approx 0.392328572515123$$$A

$$$P{\left(X \lt 1 \right)}\approx 0.35963452480553$$$A

$$$P{\left(X \leq 1 \right)}\approx 0.751963097320653$$$A

$$$P{\left(X \gt 1 \right)}\approx 0.248036902679347$$$A

$$$P{\left(X \geq 1 \right)}\approx 0.64036547519447$$$A