A manager of the company desires to estimate the average marks of personal motivation test for their staff. The staff were divided based on their department-Administration, Operation and Logistic. The...

Extracted text: A manager of the company desires to estimate the average marks of personal motivation test for their staff. The staff were divided based on their department-Administration, Operation and Logistic. The marks achieved by these staffs on their personal motivation test are given below. Department Administration Operation Logistic Number of staffs 23 48 29 Number of staffs selected 12 24 14 Average marks of motivation test 78 81 85 Population Standard deviation 3.4 2.5 3.6 a) Estimate the mean marks for all staffs and place a bound on the error of estimation. b) Suppose the mean mark for all the staffs is to be estimated again in restructuring the organization. Assuming the costs of sampling is equal for all strata, find the optimum allocation of a sample of size 45.