Question

A 78​% 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 ​(Round to the nearest tenth as​ needed.)Find the variance of the binomial distribution. (Round to the nearest tenth as​ needed.)Find the standard deviation of the binomial distribution. (Round to the nearest tenth as​ needed.)Most samples of 6 adults would differ from the mean by no more than nothing. ​(Type integers or decimals rounded to the nearest tenth as​ needed.)

Answer 1

Explanation:

Let x be a random variable representing the number of U.S. adults who think that political correctness is a problem in America today. Since it is a binomial probability distribution, the probability if success, p = 78/100 = 0.78

The probability of failure, q = 1 - p = 1 - 0.78 = 0.22

Number of samples = 6

Mean = np = 6 × 0.78 = 4.7

Variance = npq = 6 × 0.78 × 0.22 = 1.0

Standard deviation = √variance = 1.0

Most samples of 6 adults would differ from the mean by no more than 1