Referring to Exercise 7,
The article "Some Field Experience in the Use of an Accelerated Method in Estimating 28-Day Strength of Concrete" (J. of Amer. Concrete Institute, 1969: 895) considered regressing y = 28day standard-cured strength (psi) against x = accelerated strength spsid. Suppose the equation of the true regression line is y = 1800 + 1.3x.
Suppose that the standard deviation of the random deviation e is 350 psi.
a. What is the probability that the observed value of 28-day strength will exceed 5000 psi when the value of accelerated strength is 2000?
b. Repeat part (a) with 2500 in place of 2000.
c. Consider making two independent observations on 28-day strength, the first for an accelerated strength of 2000 and the second for x = 2500. What is the probability that the second observation will exceed the first by more than 1000 psi?
d. Let Y1 and Y2 denote observations on 28-day strength when x = x1 and x = x2, respectively. By how much would x2 have to exceed x1 in order that P(Y2 . Y1) = .95?