Final answer:
The standard deviation of the probability distribution of x is approximately 2.52.
Step-by-step explanation:
The standard deviation of the probability distribution of x can be calculated using the formula σ = √(n * p * (1 - p)), where n is the sample size and p is the probability of success. In this case, the probability of not visiting the physician's office is 0.32. Substituting the values, we have σ = √(15 * 0.32 * (1 - 0.32)) = 2.52.