The manager of a medical centre is concerned that some patients have to stand for long periods of time while the receptionist processes their appointment details. His goal is that the receptionist should spend no more than one minute with each patient. He requests your help in conducting a statistical analysis of the situation to see what adjustments will need to be met in order to meet this goal. a) The amount of time the receptionist spends with each patient is known to have a mean of 2 minutes and a standard deviation of 20 seconds. (i) Calculate the standard error of the mean if a sample of 15 patients is selected. Repeat for a random sample of 30 patients. 1 mark (ii) If random samples of 40 patients were selected, what proportion of the sample means would be between 90 and 150 seconds?