Three grades of jet fuel are blended to be used on long commercial flights. Each grade cost about the same and has about the same ignition or burn rate (gal/min) in a jet engine. The question is how to make the blend for the most consistent ignition rate. Assume the ignition rates of the three grades of fuel are statistically independent.

 (a) Let x₁, x₂, x₃ be random variables representing ignition rate (gal/min) for the three grades of fuel. After extensive testing (flying under different conditions) the standard deviations are found to be σ₁ = 7, σ₂ = 12 and σ₃ = 15. Explain why a blend of approximately 64% grade 1 fuel with 22% grade 2 fuel and 14% grade 3 fuel would give the most consistent ignition rate.

(b) Use c₁ = 0.64, c₂ = 0.22, and c₃ = 0.14 to compute σ_w and show that σ_w is less than each of σ₁, σ₂ and σ₃. Would you say the blended jet fuel has a more consistent ignition rate than each separate fuel? Explain.