1. A simple random sample of 80 customers is selected from an account receivable portfolio and the sample mean account balance is $1250. The population standard deviation is known to be $250. Explain

1. Construct a 95% confidence interval for the mean account balance of the population.
2. What is the margin of error for estimating the mean account balance at the 95% confidence level.
3. Construct a 95% confidence interval for the mean account balance of the population if the sample mean account balance is obtained from a random sample of 150 instead of 80.
4. d.Based on the results from a. and c., what can you say about the effect of a larger sample size on the length of the confidence interval at the same confidence level?

2.A simple random sample of 50 calls is monitored at an in-bound call center and the average length of the calls is 6.5 minutes. The population standard deviation is unknown. Instead the sample standard deviation s is also calculated from the sample and is found to be 4.5 minutes. Explain

1. Construct a 99% confidence interval (using the t-distribution) for the average length of inbound calls.
2. What is the margin of error at the 95% confidence level?
3. Do we need to make any assumption on the distribution of the length of in-bound calls at this call center? Why or why not?