Assuming the standard deviation of the payment times for all payments

Assuming the standard deviation of the payment times for all payments

Subject: Mathematics    / Statistics
Question

The 4 part question is listed below. Other needed information is:
Sample Mean= 18.11
Sample size= 65
Population Size= 7823
Standard Deviation=4.2
Assuming the standard deviation of the payment times for all payments is 4.2 days, construct a 95% confidence interval estimate to determine whether the new billing system was effective. State the interpretation of 95% confidence interval and state whether or not the billing system was effective.
Using the 95% confidence interval, can we be 95% confident that µ ? 19.5 days?
Using the 99% confidence interval, can we be 99% confident that µ ? 19.5 days?
If the population mean payment time is 19.5 days, what is the probability of observing a sample mean payment time of 65 invoices less than or equal to 18.1077 days?