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# Mathcad - UF-ESI-6321-12-01-02 - UF-ESI-6321 UF-ESI-02.xmcd...

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UF-ESI-6321 UF-ESI-6321-12-01-02.xmcd page 1 of 2 12.1.2 Suppose that the purity of a chemical solution y is related to the amount of a catalyst x through a linear regression model with β 0 123.0 := β 1 2.16 - := and with an error standard deviation σ 4.1 := ε 0 := E x ( ) β 0 β 1 x + ε + := (a) What is the expected value of the purity when the catalyst level is x 20 := E x ( ) 79.8 = (b) How much does the expected value of the purity change when the catalyst level increases by Δ x 10 := E x Δ x + ( ) E x ( ) - 21.6 - = (c) What is the probability that the purity is less than Y 60.0 := when the catalyst level is x 25 := E x ( ) 69 = Z Y x , ( ) Y E x ( ) - σ := Z Y x , ( ) 2.195 - = cnorm Z Y x , ( ) ( ) 0.0141 = Luther Setzer 1 NASA Pkwy E Stop NEM3, Kennedy Space Center, FL 32899 (321) 544-7435

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