{a} In the claims department of an insurance office various quantities are computed at the end of each day's business. On Monday, 20 claims are received for a particular class of policy. The mean claim amount is calculated to be K4,500 and the standard deviation to be K1540. On Tuesday, the claims are reviewed and one claim which was incorrectly recorded as K13,000 is now corrected to K3,000. Determine the mean and standard deviation of the corrected set of claims. (b) Last year two groups of students (part-time and distance) sat for the same 635 541 exam. The marks in the part-time group of 64 students had an average of 52 and a standard deviation of 9. The marks in the distance group of 42 students had an average of 45 and a standard deviation of 8. Calculate the average and standard deviation of the combined set of 106 students