Suppose that a recent poll found that 41% of adults believe that the overall state of moral values is poor. complete parts (a) through (c). (a) for 100 randomly selected adults, compute the mean and standard deviation of the random variable x, the number of adults who believe that the overall state of moral values is poor. the mean of x is 41. (round to the nearest whole number as needed.) the standard deviation of x is 4.9. (round to the nearest tenth as needed.) (b) interpret the mean. choose the correct answer below. a. for every 100 adults, the mean is the minimum number of them that would be expected to believe that the overall state of moral values is poor. b. for every 100 adults, the mean is the number of them that would be expected to believe that the overall state of moral values is poor. your answer is correct. c. for every 100 adults, the mean is the range that would be expected to believe that the overall state of moral values is poor. d. for every 41 adults, the mean is the maximum number of them that would be expected to believe that the overall state of moral values is poor. (c) would it be unusual if 41 of the 100 adults surveyed believe that the overall state of moral values is poor? yes no

a) μ = 41, σ = 4.9; b) For every 100 adults, the mean is the number of them that would be expected to believe the overall state of moral values is poor; c) No, it would not.

Step-by-step explanation:

This is a binomial distribution.  This is because 1) there is a fixed number of trials (100); 2) there are two outcomes (either they do feel it's poor or they don't feel it's poor); 3) each trial is independent of each other; 4) the probability of success is the same for each trial.

a) Since this is a binomial distribution, the mean is given by μ = np, where n is the number of trials and p is the probability of success.  This gives us

μ = 100(0.41) = 41

The standard deviation is given by

σ = √(npq), where n is the number of trials, p is the probability of success and q is the probability of failure.  Since p = 0.41, this makes q = 1-0.41 = 0.59; this gives us

σ = √(100(0.41)(0.59)) = √(24.19) ≈ 4.9

b) The mean tells us the average number of people out of the sample that feel the state of moral values is poor.

c) A data value that is unusual is one that is more than 2 standard deviations from the mean.  In this case, the number in question is the mean; this means it is 0 standard deviations from the mean, so it is not an unusual value.

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