Find $$$P{\left(X = 1 \right)}$$$ for binomial distribution with $$$n = 10$$$ and $$$p = 0.175$$$

Calculate the various values for the binomial distribution with $$$n = 10$$$, $$$p = 0.175 = \frac{7}{40}$$$, and $$$x = 1$$$.

Mean: $$$\mu = n p = \left(10\right)\cdot \left(\frac{7}{40}\right) = \frac{7}{4} = 1.75$$$A.

Variance: $$$\sigma^{2} = n p \left(1 - p\right) = \left(10\right)\cdot \left(\frac{7}{40}\right)\cdot \left(1 - \frac{7}{40}\right) = \frac{231}{160} = 1.44375$$$A.

Standard deviation: $$$\sigma = \sqrt{n p \left(1 - p\right)} = \sqrt{\left(10\right)\cdot \left(\frac{7}{40}\right)\cdot \left(1 - \frac{7}{40}\right)} = \frac{\sqrt{2310}}{40}\approx 1.201561484069792.$$$A

$$$P{\left(X = 1 \right)}\approx 0.309830084623023$$$A

$$$P{\left(X \lt 1 \right)}\approx 0.146062754179425$$$A

$$$P{\left(X \leq 1 \right)}\approx 0.455892838802448$$$A

$$$P{\left(X \gt 1 \right)}\approx 0.544107161197552$$$A

$$$P{\left(X \geq 1 \right)}\approx 0.853937245820575$$$A