Suppose that a recent poll found that \( 62 \% \) of adults believe that the overall state of moral values is poor. Complete parts (a) through (c). (a) For 150 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 and standard deviation of the random variable \( X \) representing the number of adults who believe that the overall state of moral values is poor, we can use the properties of a binomial distribution. The mean \( \mu \) is given by the formula: \[ \mu = n \times p \] where \( n \) is the number of trials (in this case, 150 adults) and \( p \) is the probability of success (here, \( 0.62 \)). Calculating this: \[ \mu = 150 \times 0.62 = 93 \] So, the mean of \( X \) is \( 93 \). Next, we calculate the standard deviation \( \sigma \), which is given by the formula: \[ \sigma = \sqrt{n \times p \times (1 - p)} \] Let's calculate: \[ \sigma = \sqrt{150 \times 0.62 \times (1 - 0.62)} = \sqrt{150 \times 0.62 \times 0.38} \] \[ \sigma \approx \sqrt{35.34} \approx 5.95 \] In conclusion, the mean number of adults who believe that moral values are poor is \( 93 \) and the standard deviation is approximately \( 6 \) (rounded to the nearest whole number).