1. A bank knows that the balances in customer savings accounts are normally distributed with a mean of $5,000 and a standard deviation of $1,500. Suppose the bank randomly selects a single customer to sample and records their savings account balance. What is the mean and standard deviation of the distribution? Include variables as part of the solution What is the probability that a randomly selected customer has a balance greater than $6,000? c. If a random sample of 63 customer accounts is selected, what is the mean and standard deviation of the sampling distribution of sample mean balances? Include variables as part of the solution d. Describe the shape of the sampling distribution of ????̅ (sample mean account balances) and justify your answer. e. What is the probability that the sample mean balance of the 63 customer accounts is greater than $5,300? f. How would the sampling distribution of ????̅ (sample mean account balances) change if the sample size, n, were increased from 63 to 100?