Find the mean, variance, and standard deviation of the binomial distribution with the given values of $n$ and $p$.
\[
n=80, \mathrm{p}=0.3
\]
The mean, $\mu$, is 24 . (Round to the nearest tenth as needed.)
The variance, $\sigma^{2}$, is $\square$. (Round to the nearest tenth as needed)
Answer
Final Answer: The variance, \(\sigma^{2}\), is \(\boxed{16.8}\).
Step 1 ：Given that \(n=80\) and \(p=0.3\).
Step 2 ：The mean of a binomial distribution is given by the formula \(\mu = np\).
Step 3 ：Substitute the given values into the formula to get \(\mu = 80 * 0.3 = 24\).
Step 4 ：The variance of a binomial distribution is given by the formula \(\sigma^2 = np(1-p)\).
Step 5 ：Substitute the given values into the formula to get \(\sigma^2 = 80 * 0.3 * (1 - 0.3) = 16.8\).
Step 6 ：Final Answer: The variance, \(\sigma^{2}\), is \(\boxed{16.8}\).
