Question

The waiting time in the emergency department in a large hospital is a concern for the outdoor patients. Based on the historical records of the hospital it is found that the mean and standard deviation of waiting time of patients in the emergency department are 40 minutes and 6 minutes respectively. Assume that the distribution of waiting time follows a normal model. For the waiting time of a random sample 25 patients from the population of patients in the emergency department of the hospital, answer the following questions. (a) (1 mark) What is the variable of interest in the question? (b) (3 marks) Find the probability that one randomly selected patient will wait less than 36 minutes. (C) (3 marks) What type of distribution is the sampling distribution of the waiting time of the sample means of patients? Specify the parameters of this sampling distribution for a random sample of 25 patients from the population of all patients in the emergency department in the hospital. (d) (5 marks) Find the probability that the sample mean of a random sample of 25 patients will be less than 36 minutes. (e) (2 mark) Explain the reason for the difference in your answers in parts (b) and (d).