<p>12.6. Tomatoes are packaged in a can designed to hold a nominal 20 ounces of product. Five cans sampled randomly were found to contain 28.3, 27.3, 29.1, 28.5, and 27.8 ounces of product. (a) Calculate the mean value and range of sample data, and (b) estimate the variance and standard deviation of the sampled population.</p><p>12.7. An “x-bar” control chart is developed for recording the mean value of a quality characteristic using a sample size of three. The control chart has control limits (LCL and UCL) of 1.000 and 1.020 pounds respectively. If a new sample of three items has weights of 1.023, 0.999, and 1.025, what can we say about the lot (batch) it came from?</p><p>14-7. For the project outlined in the following table, prepare (a) a bar chart, (b) an arrow network diagram, and (c) a circle (AON) network diagram. (d) What and how long is the critical path?</p><p>Task Follows Weeks Manning Task(s) Duration Level A Start 6.0 3 B Start 5.0 4 C Start 5.0 3 D A 3.0 2 E A, B 6.0 5</p><p>14-8. For the project in question 14-7: (a) provide a worker-level profile assuming that all tasks begin as early as possible; (b) repeat the profile assuming that no more than nine people are available in any week and the manning level for a task cannot change; and (c) identify the project duration in each case.</p><p>14.9. Tasks X, Y, and Z must be completed in series to complete a project. The three time estimates (a, m, and b) for each task in days are X: 30, 45, and 66 days; Y: 24, 42, and 60 </p><p> days; and Z: 26, 50, and 68 days. For each task, calculate (a) the expected time te and (b) </p><p> the standard deviation . What is the (c) expected time Te and (d) the standard deviation </p><p>T for the complete project?</p><p>14.10. If a project has an expected time of completion Te of 45 weeks with a standard deviation </p><p>T of 7 weeks, what is the probability of completing it (a) within one year (52 weeks)? (b) Within 38 weeks?</p>