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8 April, 03:23

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.

1. Find the mean of the binomial distribution (Round to the nearest tenth as needed.)

2. Find the variance of the binomial distribution. (Round to the nearest tenth as needed.)

3. Find the standard deviation of the binomial distribution. (Round to the nearest tenth as needed.)

4. 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.)

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  1. 8 April, 03:40
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    Step-by-step 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. This is a binomial distribution since the outcomes are two ways. The probability of success, p = 78/100 = 0.78

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

    n = 6

    a) Mean = np = 6 * 0.78 = 4.68

    b) Variance = npq = 6 * 0.78 * 0.22 = 1.0

    c) Standard deviation = √npq = √ (6 * 0.78 * 0.22) = 1.0

    d) The standard deviation is used to express the spread of the data from the mean. Therefore, most samples of 6 adults would differ from the mean by no more than 1.0
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