Question

find the mean, variance, and standard deviation of the binomial distribution with the given values of n and p
n = 70, p = 0.4
the mean, μ, is 28.0. (round to the nearest tenth as needed.)
the variance, σ², is □. (round to the nearest tenth as needed.)

Explanation:

Step1: Recall the formula for variance of binomial distribution

The formula for variance of a binomial distribution is \(\sigma^{2}=np(1 - p)\).

Step2: Substitute the given values \(n = 70\) and \(p=0.4\) into the formula

First, find \(1-p\): \(1 - p=1 - 0.4=0.6\).
Then, calculate \(np(1 - p)\): \(\sigma^{2}=70\times0.4\times0.6\).

$$
LATEXBLOCK0
$$

Answer:

The variance \(\sigma^{2}\) is \(16.8\)