Questions: 79% 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. Find the mean of the binomial distribution. μ= (Round to the nearest tenth as needed.)

79% 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. Find the mean of the binomial distribution. μ= (Round to the nearest tenth as needed.)
Transcript text: $79 \%$ 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. Find the mean of the binomial distribution. $\mu=$ $\square$ (Round to the nearest tenth as needed.)
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Solution

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Solution Steps

Step 1: Understanding the Problem

We are tasked with finding the mean of a binomial distribution where \( n = 6 \) (the number of trials) and \( p = 0.79 \) (the probability of success). The mean \( \mu \) of a binomial distribution can be calculated using the formula:

\[ \mu = n \cdot p \]

Step 2: Calculating the Mean

Substituting the values into the formula, we have:

\[ \mu = 6 \cdot 0.79 = 4.74 \]

Step 3: Rounding the Mean

We round the calculated mean to the nearest tenth:

\[ \mu \approx 4.7 \]

Final Answer

The mean of the binomial distribution is

\[ \boxed{\mu = 4.7} \]

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