An article considered regressing  y = 28-day standard-cured strength (psi)  against  x = accelerated strength (psi).  Suppose the equation of the true regression line is  y = 1900 + 1.3x,  and that the standard deviation of the random deviation ϵ 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? (Round your answer to four decimal places.)   (b) What is the probability that the observed

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An article considered regressing 
y = 28-day standard-cured strength (psi)
 against 
x = accelerated strength (psi).
 Suppose the equation of the true regression line is 
y = 1900 + 1.3x,
 and that the standard deviation of the random deviation ϵ 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? (Round your answer to four decimal places.)
 
(b)
What is the probability that the observed value of 28-day strength will exceed 5000 psi when the value of accelerated strength is 2600? (Round your answer to four decimal places.)
 
(c)
Consider making two independent observations on 28-day strength, the first for an accelerated strength of 2000 and the second for 
x = 2600.
 What is the probability that the second observation will exceed the first by more than 1000 psi? (Round your answer to four decimal places.)
 
(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) = 0.95?
 (Round your answer to two decimal places.)
 
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