Mathcad - UF-ESI-6321-12-01-02

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

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Unformatted text preview: 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 0 := 123.0 1 := -2.16 and with an error standard deviation := 4.1 := 0 E( x) := 0 + 1 x + (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 x := 10 E( x + 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 ) 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 UF-ESI-6321 UF-ESI-6321-12-01-02.xmcd page 2 of 2 (d) What is the probability that the purity is between Y1 := 30 and Y2 := 40 when the catalyst level is x := 40 E( x) = 36.6 Z ( Y1 , x) = -1.61 Z ( Y2 , x) = 0.829 cnorm( Z ( Y1 , x) ) = 0.0537 cnorm( Z ( Y2 , x) ) = 0.7965 cnorm( Z ( Y2 , x) ) - cnorm( Z ( Y1 , x) ) = 0.7428 (e) What is the probability that the purity of a solution with a catalyst level of x1 := 30 is smaller than the purity of a solution with a catalyst level of x2 := 27.5 E( x1) = 58.2 E( x2) = 63.6 0 - ( E( x 1 ) - E( x 2 ) ) Z := = 0.931 + cnorm( Z ) = 0.8242 2 2 Luther Setzer 1 NASA Pkwy E Stop NEM3, Kennedy Space Center, FL 32899 (321) 544-7435 ...
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Mathcad - UF-ESI-6321-12-01-02 - UF-ESI-6321...

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