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. 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.