모수 $$$n = 30$$$ 및 $$$p = 0.5$$$를 갖는 이항분포에서 $$$P{\left(X = 0 \right)}$$$를 구하시오

주어진 $$$n = 30$$$, $$$p = 0.5 = \frac{1}{2}$$$, $$$x = 0$$$에 대해 이항분포의 다양한 값을 계산하세요.

평균: $$$\mu = n p = \left(30\right)\cdot \left(\frac{1}{2}\right) = 15$$$A.

분산: $$$\sigma^{2} = n p \left(1 - p\right) = \left(30\right)\cdot \left(\frac{1}{2}\right)\cdot \left(1 - \frac{1}{2}\right) = \frac{15}{2} = 7.5$$$A.

표준편차: $$$\sigma = \sqrt{n p \left(1 - p\right)} = \sqrt{\left(30\right)\cdot \left(\frac{1}{2}\right)\cdot \left(1 - \frac{1}{2}\right)} = \frac{\sqrt{30}}{2}\approx 2.738612787525831.$$$A

$$$P{\left(X = 0 \right)}\approx 9.31323 \cdot 10^{-10}$$$A

$$$P{\left(X \lt 0 \right)} = 0$$$A

$$$P{\left(X \leq 0 \right)}\approx 9.31323 \cdot 10^{-10}$$$A

$$$P{\left(X \gt 0 \right)}\approx 0.999999999068677$$$A

$$$P{\left(X \geq 0 \right)} = 1$$$A