la] lb) Texas Watch Company {TWC} assembles watches on two assembly lines. Line 1 uses older equipmentthan Line 2. The probability of defect free watches manufactured each hour in lines 1 and 2 are .98 and .99, respectively. Each line produces 500 watches. The manager of the assembly line wants help with the following. How many defect free watches each line is likely to produces in a given hour? Specifically, find the smallest integer, k, for each line, such thatyou can be 99% sure that each line will not produce more than k defective watches per hour. Note that k could be different for lines 1 and 2 in your answer. Start with k: 0 and go up to k=19. TWC has an order for 500 watches. It plans to fill the order by packing slightly more than 500 watches from line 2, and shipping them off to the customer. Clearly, TWC wants to send as few watches as possible and still meet the order safely. It wants to be 99% sure that when the customer opens the package, there are at least 500 defective tree watches. How many watches should be packed in the shipment? Now a second customer wants 1000 watches. TWC plans to fill this order by packing slightly more than the order quantity. The package will contain the same number of watches from each of the two lines. Again, it wants to be 99% sure that at least 1000 watches are defect free. How many watches should TWC ship? Use 500 simulations to answer this. Note it is much faster to simulate small rather than large numbers. And so, simulate the number of watches with defects, rather than without defects. Assume a trial value of 510 watches made in each of the two lines. 2. An insurance company wants to determine how its annual operating costs depend on the number of home insurance {X1} and auto insurance {X2} policies. The dataset contains information for 10 branches of the insurance company. Develop a multiplicative regression model and state it using the values from the computer output- Are all the variables significant the .05 level of significance? Explain all the slope regression coefficients from the above model. Explain the Rsquare for the above model. In terms of the standard error of the regression how good is this model? Scanner data are ubiquitous these days. A North American chain of franchised grocery stores uses scanner data to evaluate its promotional activities. Scanner data were combined with data on promotions, such as instore displays and flyer distribution activities. In order to understand the amount of scanner data the store is collecting, it should be noted that [a] there are many franchised stores; {b} in each store data are collected on thousands of products; {c} data are