Suppose that a recent poll found that $$ 46 \% $$ of adults believe that the overall state of moral values is poor. Complete parts (a) through (c). (a) For 350 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 161 . (Round to the nearest whole number as needed.) The standard deviation of X is 9.3 . (Round to the nearest tenth as needed.) (b) Interpret the mean. Choose the correct answer. A. For every 350 adults, the mean is the number of adults that would be expected to believe that the overall state of moral values is poor. B. For every 350 adults, the mean is the minimum number of adults that would be expected to believe that the overall state of moral values is poor. Cor every 350 adults, the mean is the range of adults that would be expected to believe that the overall state of moral values is poor. D. For every 350 adults, the mean is the maximum number of adults that would be expected to believe that the overall state of moral values is poor. (c) Would it be unusual if 151 of the 350 adults surveyed believe that the overall state of moral values is poor? Yes No

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Given that $$ 46\% $$ of adults believe that the overall state of moral values is poor, we can calculate 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.

(a) To find the mean and standard deviation of $$ X $$, we can use the given information:
- Mean of $$ X $$ is 161
- Standard deviation of $$ X $$ is 9.3

(b) The mean of $$ X $$ represents the expected number of adults who believe that the overall state of moral values is poor out of 350 randomly selected adults. Therefore, the correct interpretation is:
A. For every 350 adults, the mean is the number of adults that would be expected to believe that the overall state of moral values is poor.

(c) To determine if it would be unusual if 151 of the 350 adults surveyed believe that the overall state of moral values is poor, we can compare this value to the mean and standard deviation calculated in part (a).

Let's calculate the z-score for 151 adults:
$$ z = \frac{X - \mu}{\sigma} $$
where:
- $$ X = 151 $$
- $$ \mu = 161 $$
- $$ \sigma = 9.3 $$

If the z-score is greater than 2 or less than -2, it would be considered unusual.
Calculate the value by following steps:
- step0: Calculate:
  $$\frac{\left(151-161\right)}{9.3}$$
- step1: Remove the parentheses:
  $$\frac{151-161}{9.3}$$
- step2: Subtract the numbers:
  $$\frac{-10}{9.3}$$
- step3: Convert the expressions:
  $$\frac{-10}{\frac{93}{10}}$$
- step4: Multiply by the reciprocal:
  $$-10\times \frac{10}{93}$$
- step5: Multiply:
  $$-\frac{10\times 10}{93}$$
- step6: Multiply:
  $$-\frac{100}{93}$$
The z-score for 151 adults is approximately -1.075269. Since the z-score is not greater than 2 or less than -2, it would not be considered unusual if 151 of the 350 adults surveyed believe that the overall state of moral values is poor.
(a) The mean of $$ X $$ is 161, and the standard deviation is 9.3. (b) The mean represents the expected number of adults who believe the overall state of moral values is poor out of 350 surveyed. (c) It would not be unusual if 151 of the 350 adults believe the overall state of moral values is poor.

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