I will appreciate your help with these questions:

1- 80 customers are selected from an account receivable portfolio and the sample mean account balance is $1250. The population standard deviation is known to be $250.

b. What is the margin of error for estimating the mean account balance at the 95% confidence level?

2-50 calls are 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.

b.What is the margin of error at the 95% confidence level?

c.Do we need to make any assumption on the distribution of the length of in-bound calls at this call center?

3.Check out times at a supermarket are between 3 to 6 minutes (180 to 720 seconds.) A survey involving a random sample of customers of the supermarket is planned and the first order of business is to decide on an appropriate sample size. The 95% level of confidence will be used.

a.What is the planning value for the population standard deviation to be used in the sample size formula for estimating the population mean check-out time?

b.How large should the sample size be if the desired margin of error is 25 seconds?

4.In a survey, the planning value for the population proportion is p* = 0.28. How large should the sample size for the survey be if the desired level of confidence is 95% and the desired margin of error is 0.035?