business statstic and probability questions

6 Business Statistic questions All questions must be answered manually— with the aid of a calculator, if necessary. Question 2 (18 marks) The general manager of a digital products manufacturer believes that 65% of all potential customers prefer to buy MP3 players with greater than 32 GB built-in memory. A random sample of 100 customers was chosen. 2 BUS B171 Business Statistics c Suppose that among the 100 customers selected, 58 of them claimed that they prefer to buy MP3 players with over 32 GB built-in memory. Construct a 95% confidence interval estimate for the true proportion of potential customers who prefer to buy MP3 players with greater than 32 GB built-in memory. (6 marks) Question 3 (15 marks) The customer services manager of a bank wishes to estimate the true average time it takes for a customer service officer to serve a customer using the dial-in hotline services. A random sample of the service time for 14 individual customers is collected. The results are listed as follows (in minutes): 2.8 1.7 2.2 1.5 2.1 1.9 2.1 1.5 2.0 2.5 1.8 2.4 1.3 2.2 a Construct a 95% confidence interval estimate for the true average time it takes to serve a customer. Keep your final answers to two decimal places. (10 marks) b Given that the service times are normally distributed and the population variance is known to be 0.25 minutes, what sample size is required if the manager wishes to be 95% confident that the sample average is correct to within 15.0± minutes of the true average service time? (5 marks) Question 4 (16 marks) The marketing director of a cosmetics corporation wishes to estimate the average monthly demand for a newly released night-mly selected. Twenty-five of them expressed the