The mean production level at the local manufacturing plant is 47.3 units for each day with standard deviation of 12.7. The plant manager will take the sample of 100 days in order to evaluate the mean production. If the mean of sample exceeds 49 units for each day, she promises to provide all employees a bonus.
(A) Compute the standard error of the sampling distribution without using finite population correction factor. What assumption must you make?
(B) How likely are the employees to enjoy the bonus promised?
(C) Represent the population and sampling distributions graphically and show the answer. (optional).