PortaCom has developed a design for a high-quality portable printer. The two key components of manufacturing cost are direct labor and parts. During a testing period, the company has developed prototypes and conducted extensive product tests with the new printer. PortaComs engineers have developed the bivariate probability distribution shown below for the manufacturing costs. Parts cost (in dollars) per printer is represented by the random variable and direct labor cost (in dollars) per printer is represented by the random variable . Management would like to use this probability distribution to estimate manufacturing costs.

	Direct Labor (y)
Parts (x)	43	45	48	Total
85	0.12	0.09	0.22	0.43
95	0.29	0.03	0.25	0.57
Total	0.41	0.12	0.47	1.00

a. Show the marginal distribution of direct labor cost and compute its expected value, variance, and standard deviation. If your answer is zero enter 0. Enter negative values as negative numbers.

	(to 2 decimals)	(to 2 decimals)	(to 2 decimals)	(to 2 decimals)	(to 3 decimals)
43
45
48

	(to 2 decimals)
	(to 2 decimals)
	(to 2 decimals)

b. Show the marginal distribution of parts cost and compute its expected value, variance, and standard deviation. Enter negative values as negative numbers.

	(to 2 decimals)	(to 2 decimals)	(to 2 decimals)	(to 2 decimals)	(to 3 decimals)
85
95

	(to 2 decimals)
	(to 2 decimals)
	(to 2 decimals)

c. Total manufacturing cost per unit is the sum of direct labor cost and parts cost. Show the probability distribution for total manufacturing cost per unit. If necessary round your answers to 2 decimals.

128
130
133
138
140
143
Total

d. Compute the expected value, variance, and standard deviation of total manufacturing cost per unit. (Note: use ). Enter negative values as negative numbers.

	(to 2 decimals)	(to 2 decimals)	(to 2 decimals)	(to 2 decimals)	(to 3 decimals)
128
130
133
138
140
143

	(to 2 decimals)
	(to 2 decimals)
	(to 2 decimals)

e. Are direct labor and parts costs independent? Why or why not? If you conclude that they are not, what is the relationship between direct labor and parts cost? Enter negative values as negative numbers.

(to 2 decimals)

Conclude that direct labor cost is - Select your answer -not independentindependentItem 73 of parts cost. They are - Select your answer -negatively correlated.positively correlated.Item 74

f. PortaCom produced printers for its product introduction. The total manufacturing cost was . Is that about what you would expect?

If it is higher or lower, what do you think may have caused it?

The total manufacturing costs of are - Select your answer -morelessItem 76 than we would have expected.