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: C. For 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

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**(a) Calculation of the Mean and Standard Deviation**

1. The problem involves a binomial experiment where:
   - $$ n = 350 $$ (the number of adults),
   - $$ p = 0.46 $$ (the probability that an adult believes moral values are poor).

2. The mean $$ \mu $$ of a binomial distribution is given by:
   $$
   \mu = np
   $$
   Substituting the values:
   $$
   \mu = 350 \times 0.46 = 161
   $$
   (Rounded to the nearest whole number.)

3. The standard deviation $$ \sigma $$ is given by:
   $$
   \sigma = \sqrt{np(1-p)}
   $$
   First, compute the product inside the square root:
   $$
   np(1-p) = 350 \times 0.46 \times 0.54 = 86.94
   $$
   Then, take the square root:
   $$
   \sigma = \sqrt{86.94} \approx 9.3
   $$
   (Rounded to the nearest tenth.)

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**(b) Interpretation of the Mean**

The mean $$ \mu = 161 $$ represents the expected number of adults (out of 350) who believe that the overall state of moral values is poor. This corresponds to choice:

**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.**
**(a) Mean and Standard Deviation** - **Mean (μ):** 161 adults - **Standard Deviation (σ):** 9.3 **(b) Interpretation of the Mean** 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.

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