BBM203 Business Statistics September 2022 1. Time spent sewing a customer at a cafe is normally distributed, with y = '7 minutes and a = 1.8 minutes. (a) If you select a random sample of duration serving twenty five (25) customers, determine the probability that the sample mean is between 6.8 and 7.2 minutes. [9 marks] (b) If you select a random sample of 144 customers, determine the probability that the sample mean is between 6.8 and 7.2 minutes. [6 marks] (c) Explain the difference in the results of (i) and (ii). [6 marks] 2. A factory manager collected a sample of ten (10) packets of 3-in-1 coffee and the weights (in grams) of each packet are recorded as follow: 25 23 26 28 24 21 26 24 25 2? Calculate (a) the mean weight of a packet of 3-in-1 coffee. [3 marks] (b) the sample standard deviation of the data collected. [6 marks] (0) nd a 90% condence interval for the weights of the 3-in-1 coffee. [6 marks] 3. A service counter manager wishes to ensure that an average of 16 seconds to serve a customer. In order to analyse the efficiency of the service process, he takes a random sample of 56 customers. The mean service time of the sample is 15.8 seconds. Assume that the population standard deviation is 0.8 seconds. (a) State the null and the alternative hypotheses for the test. [4 marks] (b) Use the p-value approach to test the manager's concern at a = 0.05. [8 marks] (0) Confirm your result in (ii) by using the critical value approach. [6 marks] (d) State the recommendation that the manager can present to the company. [3 marks]