Time lost due to employee absenteeism is an important problem for many companies. The human resources department of Western Electronics has studied the distribution of time lost due to absenteeism by individual employees. During 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 probability that the number of absences for this one employee would exceed 25 days?
b) If many samples of 36 employees each are taken and sample means computed, a distribution of sample means would result. What would be the mean, standard deviation and shape of the distribution of sample means for samples of size 36? Give reasons for your answers.
c) A group of 36 employees is selected at random to participate in a program that allows a flexible work schedule, which the human resources department hopes will decrease the employee absenteeism in the future. What is the probability that the mean for the sample of 36 employees randomly selected for the study would exceed 25 days?