Statistic

The director of human resources of a large commercial firm is studying
the weekly average time off of employees. A random sample of 20
employees is selected and the corresponding time off in hours during a
particular week is given as follows:

4.0 1.8 5.9 2.8 2.5 2.6 3.5 1.8 4.2 2.0
2.7 4.8 6.0 1.6 3.5 4.1 2.7 3.2 1.0 3.6

a In constructing a confidence interval for the true weekly average time
off of employees, explain briefly what distribution has to be used?
What initial assumption(s) must be made?

b Construct a 95% confidence interval for the true weekly average time off of employees. Keep an accuracy of two decimal places.