Step 1 :The problem provides us with a linear equation \(y=0.87 x+4.01\), where \(x\) is the number of automatic weapons in thousands and \(y\) is the number of murders per 100,000 residents.
Step 2 :For part A, we are asked to find the expected number of murders per 100,000 residents in a state with 2.9 thousand automatic weapons. We can find this by substituting \(x=2.9\) into the equation and solving for \(y\).
Step 3 :Substituting \(x=2.9\) into the equation gives us \(y=0.87(2.9)+4.01\).
Step 4 :Solving the equation gives us \(y=6.533\). So, the expected number of murders per 100,000 residents in a state with 2.9 thousand automatic weapons is \(\boxed{6.533}\).
Step 5 :For part B, we are asked to find the expected number of murders per 100,000 residents in a state with 4.2 thousand automatic weapons. We can find this by substituting \(x=4.2\) into the equation and solving for \(y\).
Step 6 :Substituting \(x=4.2\) into the equation gives us \(y=0.87(4.2)+4.01\).
Step 7 :Solving the equation gives us \(y=7.664\). So, the expected number of murders per 100,000 residents in a state with 4.2 thousand automatic weapons is \(\boxed{7.664}\).