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Find $$$P{\left(X = 0 \right)}$$$ for binomial distribution with $$$n = 30$$$ and $$$p = 0.5$$$
Your Input
Calculate the various values for the binomial distribution with $$$n = 30$$$, $$$p = 0.5 = \frac{1}{2}$$$, and $$$x = 0$$$.
Answer
Mean: $$$\mu = n p = \left(30\right)\cdot \left(\frac{1}{2}\right) = 15$$$A.
Variance: $$$\sigma^{2} = n p \left(1 - p\right) = \left(30\right)\cdot \left(\frac{1}{2}\right)\cdot \left(1 - \frac{1}{2}\right) = \frac{15}{2} = 7.5$$$A.
Standard deviation: $$$\sigma = \sqrt{n p \left(1 - p\right)} = \sqrt{\left(30\right)\cdot \left(\frac{1}{2}\right)\cdot \left(1 - \frac{1}{2}\right)} = \frac{\sqrt{30}}{2}\approx 2.738612787525831.$$$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