Referring to Exercise 7, suppose that the standard deviation of the random deviation 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?
Reference 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) considx ered regressing y = 28-day standard-cured strength (psi) against x = accelerated strength (psi). Suppose the equation of the true regression line is y = 1800 1 1.3x .
a. What is the expected value of 28-day strength when accelerated strength= 2500 ?
b. By how much can we expect 28-day strength to change when accelerated strength increases by 1 psi?
c. Answer part (b) for an increase of 100 psi.
d. Answer part (b) for a decrease of 100 psi.
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