Question

Suppose that a recent poll found that 68% of adults believe that the overall state of moral values is poor.

​(a) For 100 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.

Answer 1

To find the mean and standard deviation of the random variable X, we can use the formulas for the mean and standard deviation of a binomial distribution. The mean of X is 68, and the standard deviation of X is approximately 4.70.

Step-by-step explanation:

To find 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, we can use the formulas for the mean and standard deviation of a binomial distribution.

The mean (µ) of X is given by µ = n * p, where n is the sample size and p is the probability of success. In this case, n = 100 and p = 0.68. So µ = 100 * 0.68 = 68.

The standard deviation (σ) of X is given by σ = sqrt(n * p * (1 - p)). So σ = sqrt(100 * 0.68 * (1 - 0.68)) = sqrt(22.08) ≈ 4.70.