A small family hotel employs just one receptionist. Over the past six weeks the receptionist worked the following hours of overtime: 19 hours, 22 hours, 23 hours, 25 hours, 27 hours
and 28 hours.

(a) Find the mean and standard deviation of the overtime that the receptionist worked.

(b) If a part-time receptionist had been employed, who worked 19 hours each week, what would the mean and standard deviation of the remaining overtime have been?

(c) If the part-time receptionist had worked 23 hours each week, what would be the mean and standard deviation of the overtime?

(d) The receptionist is paid £200 for a 40-hour week, and overtime is paid at time and a half. The plan is to pay the part-time receptionist at the same basic hourly rate. Should the hotel employ the part-time receptionist for 19 hours, or for 23 hours each week?