Final answer:
The probability of a sample mean greater than 64 children cannot be determined without additional data such as the population standard deviation; therefore, we cannot provide an accurate probability value or choose from the provided options.
Step-by-step explanation:
The question pertains to probability and asks for the likelihood of a random sample of 10 days having a mean greater than 64 children being dropped off at a daycare center. Since we do not have specific information about the population standard deviation or the individual sample means (other than the average of this sample), we cannot directly calculate the probability. To answer this probability question accurately, we would typically use the Central Limit Theorem which states that the sampling distribution of the sample mean will be normally distributed if the sample size is large enough. Assuming a normal distribution, we would need additional data such as the population standard deviation and use this to calculate the z-score for a mean of greater than 64, and then find the corresponding probability. However, since this data is not provided, this specific question cannot be conclusively answered with the provided options (A, B, C, or D).