A. Calculate the width for a 90% confidence interval estimate of the population mean assuming sample size is 50, sample mean is 80, sample variance is 121, and population size is 800. Be sure to first check all assumptions. Show all your work.

B. What are the values of the LCL and the UCL to estimate the population mean if the sample size is 144, sample standard deviation is 24, the sample mean is 75, and the risk is 1%. Show all your work.

C. It is important for airlines to follow the published scheduled departure times of flights. Suppose that one airline that recently sampled the records of 250 flights originating in Boston found that 30 flights were delayed for severe weather, 10 flights were delayed for maintenance concerns, and the rest of the flights were on time. Calculate the percentage of all flights from Boston delayed due to severe weather using a 95% confidence interval. Be sure to check all assumptions, as well as show all your work.

D. A local tutoring service offers help to children struggling with basic mathematics. This company was founded in mid-2020 by a group of retired teachers who were concerned that online learning during the COVID pandemic has hindered students' learning and understanding of the very basics of mathematics . Currently, the company has locations in Daytona Beach, Gainesville, and Orlando. The company accepts American Express and Visa for payment of services.

From a random sample of 140 payments, a confidence interval for the proportion of customers who pay for preparations for the SAT exams using an American Express card extends from 0.40 to 0.48. What is the confidence level of this interval? Show your work.

E. A random sample of 5 salespersons who attended a motivational course on sales techniques was monitored 4 months before and 4 months after the course. The values of sales (in thousands of dollars) generated by these salespeople before and after the motivational course are listed below. What is the margin of error for a 98% confidence interval estimate for the difference between the population mean sales before and after completing this motivational course. Use Data Analysis in Excel.

Salesperson: 1 2 3 4 5

Before: 230 232 225 231 238

After: 245 265 236 229 251