How do you find the mean variance, and standard deviation of the binomial distribution with $n = 70$ $n= 70$ and $p = .2$ $p=.2$ ?

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Answer 1 · 2018-02-19T16:47:42

$E (X) = 14$ $E(X)=14$

$V A R (X) = 11.2$ $VAR(X)=11.2$

$s d = 3.35 (2 d p)$ $sd=3.35(2dp)$

for a Binomial distribution

$X ~ B (n, p)$ $X~B(n,p)$

mean, or expected value $E (X) = n p$ $" "E(X)=np$

variance $V a r (X) = n p (1 - p)$ $" "Var(X)=np(1-p)$

so in this case we have

$X ~ B (70, 0.2)$ $X~B(70,0.2)$

$:.E(X)=70xx0.2=14$

$Var(X)=70xx0.2xx0.8=11.2$

$sd=sqrt("Var(X)")=sqrt11.2=3.35(2dp)$

How do you find the mean variance, and standard deviation of the binomial distribution with n= 70n=70n= 70 and p=.2p=.2p=.2?