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 $$ \square $$. (Round to the nearest tenth as needed.)

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The random variable $$ X $$ (the number of adults who believe that the overall state of moral values is poor) follows a binomial distribution with parameters $$ n = 350 $$ and $$ p = 0.46 $$.

**Step 1. Compute the mean**

The mean is given by:
$$
\mu = np
$$
Substitute $$ n = 350 $$ and $$ p = 0.46 $$:
$$
\mu = 350 \times 0.46 = 161
$$

**Step 2. Compute the standard deviation**

The standard deviation is given by:
$$
\sigma = \sqrt{np(1-p)}
$$
Substitute the values:
$$
\sigma = \sqrt{350 \times 0.46 \times (1 - 0.46)}
$$
Simplify by calculating $$ 1 - 0.46 $$:
$$
\sigma = \sqrt{350 \times 0.46 \times 0.54}
$$
First, compute the product:
$$
350 \times 0.46 = 161
$$
Then:
$$
161 \times 0.54 = 86.94
$$
Now, take the square root:
$$
\sigma = \sqrt{86.94} \approx 9.3
$$

Thus, the standard deviation of $$ X $$ is $$ 9.3 $$ (rounded to the nearest tenth).
The standard deviation of $$ X $$ is $$ 9.3 $$.

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