Alpha Family and Life Clinic has been operating since 1995. The mean waiting time for the patient during peak hours (09.00am to 11.30am) is 40 minutes, with a standard deviation of 15.5 minutes as compared to off -peak hours (11.30am to 2.00pm) which is 15 minutes, with a standard deviation of 5 minutes. (a) The distribution for both peak and off-peak hours are defined as follows. Let X be the waiting time during peak hours for patient. X - NA. 15.5) Let Y be the waiting time during off peak hours for patient. Y - N(15, 87) Fill in the missing values of A and B. A B A/ (b) Find the probability that a patient has to wait longer than an hour from 09.30am to 11.00am. Leave your answer to the nearest 4 decimal places. (c) Based on your answer in part (b) above, is it rare for a patient to wait longer than an hour if the patient reaches the clinic between 09.30am and 11.00am? Yes/No (d) Mr Albert is unwell, and he reached the clinic at 12.45pm. Find the probability that Mr Albert has to wait less than 20 mins. Leave your answer to the nearest 4 decimal places. (e) The nurse told him that there is an 80% chance or more that his waiting time is less than 20min. Based on your answer in part (d) above, is the nurse estimation correct? Yes/NoNote that in this question, if an event has a probability of less than 5%, it is considered a rare event. For the past many years, the mean expenditure of shoppers at a store in a town is $59.30 with a standard deviation of $22.70. A marketing agent intends to observe the expenditure of 40 shoppers randomly at the store. The manager of the store claims that the expenditure of the shoppers follows a normal distribution. Let X be the expenditure of a shopper and X be the sample mean expenditure of 40 shoppers. Since X is normal, X is also normal. Hence, the sampling distribution of the sample mean expenditure of 40 shoppers is as follows: X ~ NA. (a) The sampling distribution of the sample mean expenditure of 40 shoppers is described above. Fill in the missing values of A, B and C below. A $ B C $ (b) What is the standard error of the sampling distribution of the sample means? Leave your answer to the nearest three decimal places. $ (c) What is the probability that the mean expenditure of 40 shoppers is $64.20 or more? Leave your answer in the nearest four decimal places. (d) What is the probability that the mean expenditure of 40 shoppers is $50.40 or less ? Leave your answer in the nearest four decimal places. (e) Based on your answer in part (d), is it rare for a sample of 40 shoppers to have a mean expenditure of $50.40 or less? Yes/No