Time lost because of employee absenteeism is an important problem for various companies. The human resources department of Western Electronics has studied the allocation of time lost due to absenteeism by individual employees. Through a one-year period, the department found a mean of 21 days and a standard deviation of 10 days based on data for all the employees.

a) If you pick an employee at random, what is the possibility that the number of absences for this one employee would exceed 25 days?

b) If various samples of 36 employees each are taken and sample means computed, a distribution of sample means could result. What could be the mean, standard shape and deviation of the distribution of sample means for samples of size 36?

c) A group of 36 employees is chosen at random to participate in a program that allows a flexible work schedule, which the human resources department hopes may decrease, the employee absenteeism in the future. What is the possibility that the mean for the sample of 36 employees arbitrarily selected for the study would exceed 25 days?