Abstract: Let the liquid propellant rocket engine parameter X be the Normal probability distribution of μ and σ2, σ2 = σA2 + σE2, where σE2 is the engine run to run variance and σA2 is the engine to engine variance. The design criteria of the rocket engine are: "μ∈[μL,μU]" and "σ≤B", where μL and μU are kNown as the lower and the upper bounds of μ. B2 is the upper bound of σ2. The Inter-agency Chemical Rocket Propulsion Group of U. S. A. had given the formula of μ （the point estimate of μ） and the formula of σ （σ2 is the point estimate of σ2） from experimental values. But μ∈[μL, μU] and σ≤B are Not equivalent to μ∈[μL,μU] and σ≤B. This paper considers the problem of setting confidence intervals to the μ and σ for assigned confidence coefficient γ. μ lies in the interval , where σ2 lies in the interval [] ,where