Complete Chapter 4 problems 67 and 78 from page 204 and 206

Complete Chapter 4 problems 67 and 78 from page 204 and 206 at the end of the chapter. Refer to the associated files: P04_67.xlsxfor problem 67 and P04_78.xlsxfor problem 78. . Each year the employees at Zipco receive a $0, $2000, or $4500 salary increase. They also receive a merit rating of 0, 1, 2, or 3, with 3 indicating outstanding performance and 0 indicating poor performance. The joint probability distribution of salary increase and merit rating is listed in the file P04_67.xlsx. For example, 20% of all employees receive a $2000 increase and have a merit rating of 1. Find the correlation between salary increase and merit rating. Then interpret this correlation. 78. A manufacturing plant produces two distinct products, A and B. The cost of producing one unit of A is $18 and that of B is $22. Assume that this plant incurs a weekly setup cost of $24,000 regardless of the number of units of A or B produced. The means and standard deviations of the weekly production levels of A and B are given in the P04_78.xlsx. a. Assuming that the weekly production levels of A and B are independent, find the mean and standard deviation of this plant’s total weekly production cost. Between which two total cost figures can you be about 68% sure that this plant’s actual total weekly production cost will fall? b. How do your answers in part a change if you discover that the correlation between the weekly production levels of A and B is actually 0.29? Explain the differences in the two sets of results.