Suppose that the purity of a chemical solution y is related to the amount of a catalyst x through a linear regression model with β0 = 123.0. β1 = -2.16. and with an error standard deviation σ = 4.1.
(a) What is the expected value of the purity when the catalyst level is 20?
(b) How much does the expected value of the purity change when the catalyst level increases by 10?
(c) What is the probability that the purity is less than 60.0 when the catalyst level is 25?
(d) What is the probability that the purity is between 30 and 40 when the catalyst level is 40?
(e) What is the probability that the purity of a solution with a catalyst level of 30 is smaller than the purity of a solution with a catalyst level of 27.5?