A bank manager wants to obtain the following information regarding the employees in the finance department; a) The probability that the employee will serve in the department more than 5 years if the average service is 8 years and the populations standard deviation is known to be 2 years. b) What is the time that at least 99% of the employee are working in the department. c) To estimate the 95% confidence interval of the employees true mean time with the finance department, a sample of 25 employees is selected and the mean and standard deviation were 6 and 1 years respectively. Calculate LCL and UCL. d) How large a sample should be taken, using part (a) details, so that the error is less than 6 months with 95% confidence? e) From a sample of 25 employees, information as in part (a), it was found that 15 employee have been with the department more than 4 years. The bank manager wanted to estimate, at 90% confidence interval, the true proportion of employees with the department for more than 4 years.