This question: 7 poini(s) possiole Suppose that a recent poll found that $58 \%$ of adults believe that the overall state of moral values is poor, Complete parts (a) through (c). The mean of $\mathrm{X}$ is $\square$. (Round to the nearest whole number as needed.) The standard deviation of $\mathrm{X}$ is $\square$. (Round to the nearest tenth as needed.) (b) Interpret the mean. Choose the correct answer below. A. For every 300 adults, the mean is the number of them that would be expected to believe that the overall state of moral values is poor. B. For every 300 adults, the mean is the minimum number of them that would be expected to believe that the overall state of moral values is poor. C. For every 300 adults, the mean is the range that would be expected to believe that the overall state of moral values is poor. D. For every 174 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 162 of the 300 adults surveyed believe that the overall state of moral values is poor? Yes No Next

Step 1 ：Given that the number of adults surveyed (n) is 300 and the probability of an adult believing that the overall state of moral values is poor (p) is 0.58.

Step 2 ：The mean of a binomial distribution is given by np. Substituting the given values, we get \(mean = np = 300 \times 0.58 = 174\).

Step 3 ：The standard deviation of a binomial distribution is given by \(\sqrt{np(1-p)}\). Substituting the given values, we get \(std\_dev = \sqrt{300 \times 0.58 \times (1-0.58)} = 8.5\).

Step 4 ：For part (b), the mean of a distribution is the expected value. Therefore, for every 300 adults, the mean is the number of them that would be expected to believe that the overall state of moral values is poor.

Step 5 ：For part (c), we calculate the z-score of 162. The z-score is given by \((x - mean) / std\_dev\). Substituting the given values, we get \(z\_score = (162 - 174) / 8.5 = -1.4\).

Step 6 ：Since the z-score of 162 is within the usual range (within 2 standard deviations of the mean), it would not be unusual if 162 of the 300 adults surveyed believe that the overall state of moral values is poor.

Step 7 ：Final Answer: The mean of X is \(\boxed{174}\). The standard deviation of X is \(\boxed{8.5}\). For part (b), the correct answer is A. For every 300 adults, the mean is the number of them that would be expected to believe that the overall state of moral values is poor. For part (c), it would not be unusual if 162 of the 300 adults surveyed believe that the overall state of moral values is poor. The answer is \(\boxed{No}\).