Question

76% of u.s. adults think that political correctness is a problem in america today. you randomly select six u.s. adults and ask them whether they think that political correctness is a problem in america today. the random variable represents the number of u.s. adults who think that political correctness is a problem in america today. answer the questions below.
find the mean of the binomial distribution.
μ = 4.6 (round to the nearest tenth as needed.)
find the variance of the binomial distribution.
σ² = □ (round to the nearest tenth as needed.)

Explanation:

Step1: Identify the parameters of the binomial distribution

For a binomial distribution, the mean is $\mu = np$, and the variance is $\sigma^{2}=np(1 - p)$. Here, $n = 6$ (number of trials, i.e., number of adults selected) and $p=0.76$ (probability of success, i.e., probability that an adult thinks political correctness is a problem).

Step2: Calculate the variance

We know $n = 6$, $p = 0.76$, and $1-p=1 - 0.76=0.24$.
Using the formula $\sigma^{2}=np(1 - p)$, we substitute the values:
$\sigma^{2}=6\times0.76\times0.24$
First, calculate $6\times0.76 = 4.56$.
Then, $4.56\times0.24=\frac{456}{100}\times\frac{24}{100}=\frac{456\times24}{10000}=\frac{10944}{10000}=1.0944$

Answer:

Rounding $1.0944$ to the nearest tenth, we get $\sigma^{2}=1.1$