A company 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. The company's engineers have developed the bivariate probability distribution shown below for the manufacturing costs. Parts cost (in dollars) per printer is represented by the random variablexand direct labor cost (in dollars) per printer is represented by the random variabley. Management would like to use this probability distribution to estimate manufacturing costs.

Parts (x)Direct Labor (y)Total434548850.050.20.20.45950.250.20.10.55Total0.300.40.31.00(a)

Show the marginal distribution of direct labor cost and compute its expected value (in dollars), variance, and standard deviation (in dollars). (Round your answer for standard deviation to the nearest cent.) Need Help with E the covariance

Marginal Distribution of Direct Labor Costyf(y)

yf(y)

yE(y)

(yE(y))²

(yE(y))²f(y)

43

45

48

Var(y) =

E(y) =

dollars

_y=

dollars

(b)

Show the marginal distribution of parts cost and compute its expected value (in dollars), variance, and standard deviation (in dollars). (Round your answer for standard deviation to the nearest cent.)

Marginal Distribution of Parts Costxf(x)

xf(x)

xE(x)

(xE(x))²

(xE(x))²f(x)

85

95

Var(x) =

E(x) =

dollars

_x=

dollars

(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.

z=x+y

f(z)

128

130

133

138

140

143

Total1.00

(d)

Compute the expected value (in dollars), variance, and standard deviation (in dollars) of total manufacturing cost per unit. (Round your answer for standard deviation to two decimal places.)

expected value

dollarsvariance

standard deviation

dollars

(e)

Are direct labor and parts costs independent? Why or why not?

Since the covariance equals

, which

---Select---

is

is not

equal to zero, we can conclude that direct labor cost

---Select---

is

is not

independent of parts cost.

If you conclude that direct labor and parts costs are not independent, what is the relationship between direct labor and parts cost?

There is a positive correlation between the costs of direct labor and parts.

There is a negative correlation between the costs of direct labor and parts.

The costs of direct labor and parts are independent.

(f)

The company produced1,600printers for its product introduction. The total manufacturing cost was $198,350. Is that about what you would expect?

The expected manufacturing cost for 1,600 printers is $

which is

---Select---

lower than

higher than

equal to

$198,350.

If it is higher or lower, what do you think may have caused it? (Select all that apply.)

A supplier increased the cost of one of the more common printer parts this company uses in the manufacturing process.

At first there was a steep learning curve, but as more printers were manufactured direct labor costs decreased.

There was an increase in the cost of direct labor due to an influx of many new employees.

The expected manufacturing cost is equal to $198,350.