An article considered regressing y = 28-daystandard-cured strength (psi) against x =accelerated strength (psi). Suppose the equation of the trueregression line is  y = 1900 +1.4x,
and that the standard deviation of the random deviationϵ is 350 psi.
(a)
What is the probability that the observed value of 28-daystrength will exceed 5000 psi when the value of acceleratedstrength is 2000? (Round your answer to four decimal places.)
(b)
What is the probability that the observed value of 28-daystrength will exceed 5000 psi when the value of acceleratedstrength is 2500? (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 secondfor
x = 2500.
What is the probability that the second observation will exceedthe first by more than 1000 psi? (Round your answer to four decimalplaces.)
(d)
Let Y1 andY2 denote observations on 28-daystrength when x = x1and x = x2,respectively. By how much would x2have to exceed x1 in order thatP(Y2 >Y1) = 0.95?(Round your answer to twodecimal places.)
