Consider the linear regression model y = 5 + 0.9x, with = 1.4, which relates the

Question:

Consider the linear regression model y = 5 + 0.9x, with σ = 1.4, which relates the air content of a concrete sample x to the porosity of the sample y.
(a) What is the expected value of the porosity for a concrete sample with an air content of 20?
(b) How much does the expected value of the porosity decrease as the air content is reduced by 5?
(c) What is the probability that a concrete sample with an air content of 25 has a porosity no larger than 30?
(d) What is the probability that four independent samples of concrete each with an air content of 15 have an average porosity between 17 and 20?