Last year a company initiated a program to compensate its employees for unused s

Question

Last year a company initiated 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 allotted sick days?" Before last year, employees averaged 7 sick days per year, with a standard deviation of 2. Assuming these parameters did not change last year, find the approximate probability that the sample mean number of sick days used by 100 employees chosen at random was less than or equal to 6.4 last year.

Suppose the sample mean for the 100 employees was, in fact, 6.4. How would you interpret this result (Be sure to relate calculations in context of this problem)?

Explanation / Answer

The probability is
P(xbar<6.4)
=P((xbar-mean)/(s/n) <(6.4-7)/(2/10))

=P(Z<-3)

=0.0013 (check standard normal table)

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