Final answer:
To determine if the distribution of checking account balances approximates a normal distribution, we need to calculate the mean and standard deviation of a sample and compare it to the theoretical values. Without access to the sample data or additional information, it is not possible to answer the specific questions.
Step-by-step explanation:
The question asks whether it is reasonable that the distribution of checking account balances approximates a normal distribution. To determine this, we need to calculate the mean and standard deviation for a sample of 60 customers and compare it to the actual data. If the sample mean and standard deviation match the theoretical mean and standard deviation of a normal distribution, then it is reasonable to assume that the distribution of checking account balances approximates a normal distribution.
However, without access to the sample data or any additional information, it is not possible to determine the mean and standard deviation for the sample of 60 customers or compare it to the actual data. To answer the questions regarding the normal approximation to the binomial, probability, z-scores, and the central limit theorem, we would need more specific information or data.