4. Section 12.1 Suppose the expected cost (y) of a production run is related to

Question

4. Section 12.1 Suppose the expected cost (y) of a production run is related to the size of the run (x) 4000+10z. Let Y denote an observation on the cost of a run. Suppose size and by the equation y cost are related according to this simple lincar regression model. (a) What is the expected cost when the size of the run is 150 units? (b) By how much do you expecet the cost to increase,if the size of the run is increased by 10 units? (c) Suppose that the standard deviation of the random error e is 8250. What is the probability that the cost of a production run of 150 units will cost more than $6000? (d) Suppose the cost is observed from a production run of 200 units, and then is observed again from a production run of 250 units. What is the probability that this second observation exceeds the first by more than $1500?

Explanation / Answer

1) y= 4000 +10x

when x = 150

y = 4000 + 10*150 = 5500

b)

if x is increased by 10 , y is increased by 10*10 = 100

c) mean = 5500 , sd = 250

P(X > 6000)

P(Z>(6000 -5500)/250)

= P(Z> 2)

= 0.0228

d) when x1 = 200 ,y1^ = 6000, sd(y1) = 250

x2 = 250, y2^ = 6500, sd(y2) = 250

E(Y2 - Y1) = 500

sd(Y2-Y1) = 250*sqrt(2)

P((Y2 - Y1) > 1500)

=P(Z >(1500 -500)/(250*sqrt(2)))

=P(Z> 2.82842)

= 0.0023

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