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Question 1 A large shipping company recorded the number of tons shipped weekly across the pacific for 50 weeks. The data is presented in the table below. 522 417 538 407 430 373 479 392 429 544 494 587 631 629 564 624 456 412 552 426 590 608 538 421 520 482 452 369 477 513 413 563 499 680 586 511 404 597 652 608 497 620 527 375 656 393 534 535 516 610 1.1 Arrange the above data in a less-than cumulative distribution using seven classes of equal width. 1.2 Use the distribution in 1.1 to determine the mean, median and mode. 1.3 Draw to scale, the less-than ogive of the above distribution. 1.4 Use the graph drawn in 1.3 to determine: 1.4.1 the 70th percentile. 1.4.2 the mid 70% range. Question 2 A company supplies specialized, high-tensile pins to a customer. It uses an automatic lathe to produce the pins. Due to factors such as vibration, temperature and wear and tear, the lengths of the pins are normally distributed with a mean of 25.30 mm and a standard deviation of 0.45 mm. The customer will only buy those pins with lengths in the interval 25.00 Â± 0.50 mm. 2.1 What percentage of the pins will be acceptable to the customer? 2.2 In order to improve the percentage accepted, management considers adjusting the population mean and standard deviation of the length of the pins. If the lathe can be adjusted to have any desired mean of the lengths, what should it be adjusted to? Why? 2.3 Suppose that the mean (25.30 mm) cannot be adjusted but the standard deviation can be reduced. Calculate the maximum reduction in the standard deviation that would make 85% of the pins acceptable? 2.4 The production manager then considers the costs involved. The cost of resetting the machine to adjust the population mean involves engineering costs and the cost of production time lost. The cost of reducing the population standard deviation involves, in addition to these costs, the cost of overhauling the machine and reengineering the process. Assume it costs $150×2 to decrease the standard deviation by (x/40) mm. Find the cost of reducing the standard deviation to the values found in 2.3. Question 3 The president of a company that manufactures air conditioners is considering switching his supplier of condensers. Supplier A, the current producer of condensers for the manufacturer, prices its product 5% higher than supplier B does. Because the president wants to maintain his company’s reputation for quality, he wants to be sure that supplier B’s condensers last at least as long as supplier A’s condensers. After a careful analysis, the president decided to retain supplier A if there is sufficient statistical evidence that supplier A’s condensers last longer, on average than supplier B’s condensers. In an experiment, 15 randomly-selected midsize cars were equipped using type-A condensers while another 15 randomly-selected midsize cars were equipped with type-B condensers. The number of kilometers (in thousands) driven by each car before the condenser broke down is displayed in the table below. Supplier A Supplier B 156 109 146 75 93 131 152 131 80 129 111 147 107 78 118 124 115 86 125 127 108 111 97 146 142 114 160 136 102 98 Carry out a hypothesis test, at 5% significance level, to determine whether the president should retain supplier A. Question 4 The quarterly earnings (in $m) of a large soft-drink manufacturer has been recorded for the years 2008 – 2011. The data is listed in the table below. 2008 2009 2010 2011 1st Quarter 52 57 60 66 2nd Quarter 67 75 77 82 3rd Quarter 85 80 84 98 4th Quarter 54 61 63 67 4.1 Plot a time-series graph to represent the above data

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