Suppose the expected cost of a production run is related to

Suppose the expected cost of a production run is related to the size of the run by the equation y = 4000 + 10x. Let Y denote an observation on the cost of a run. If the variables size and cost are related according to the simple linear regression model, could it be the case that P(Y > 5500 when x = 100) = .05 and P(Y > 6500 when x = 200) = .10? Explain.

Solution

For the given linear model y = 4000 + 10 x the value of cost at x=100 is y=5000 and when x= 200 and y=6000.

in both situations the value of y is always less than the 5500 and 6500 for x=100 and x=200 respectively. corresponding probability is also very less,

p(y>5500, x=100) = 0.05 and p(y>6500, x=200)= 0.10.