Exercise 5 The "House of Blues" in Boston is planning its budget for next year. In estimating the security man-hours needed for concerts, the average length of concerts is required.

Using a random sample of n = 36 previous concerts, the sample mean duration is x = 110 minutes, while the population standard deviation is o = 20 minutes. Determine the 95% confidence interval for the true mean duration u of concerts using the sample data. (a) Construct the 95% confidence interval by hand. (b) Construct the 95% confidence interval in Minitab: 1 Open the 1-sample Z dialog box. * Minitab 19 (Mac and PC): Stat > Basic Statistics > 1-Sample Z * Minitab Express Mac: Statistics > 1-Sample Inference > Z * Minitab Express PC: STATISTICS > One Sample > Z 2 From the drop-down list, select Summarized data. 3 In Sample size, enter 36. 4 In Sample mean, enter 110. 5 In Known standard deviation, enter 20. 6 Click OK.