Suppose that a recent poll found that \( 51 \% \) of adults believe that the overall state of moral values is poor. Complete parts (a) through (c). (a) For 200 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 \( \square \). (Round to the nearest whole number as needed.)

To find the mean of the random variable \( X \), you can use the formula for the mean of a binomial distribution, which is given by \( \mu = n \cdot p \), where \( n \) is the number of trials (in this case, 200 adults) and \( p \) is the probability of success (51% or 0.51). So, the mean \( \mu = 200 \cdot 0.51 = 102 \). Next, to compute the standard deviation of \( X \), you use the formula for the standard deviation of a binomial distribution, which is \( \sigma = \sqrt{n \cdot p \cdot (1-p)} \). Thus, \( \sigma = \sqrt{200 \cdot 0.51 \cdot (1 - 0.51)} = \sqrt{200 \cdot 0.51 \cdot 0.49} \approx \sqrt{49.98} \approx 7.07 \). Therefore, the mean of \( X \) is \( 102 \) and the standard deviation is approximately \( 7 \) when rounded to the nearest whole number.