Last year a company began a program to compensate its employees for unused sick days, paying each employee a bonus of one-half the usual wage earned for each unused sick day. The question that naturally arises is: "Did this policy motivate employees to use fewer sick days?"

The company decides to answer this question by taking a random sample of 100 employees to determine the mean sick days the employees used after the institution of the policy.

a) Explain why we can assume the shape of the sampling distribution of the mean sick days for employees of the company is normal.

b) Calculate the standard error of the mean if the company has 1500 employees and the sample results indicate a mean of 9.8 sick days and a standard deviation of 1.6 sick days.